{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "Chapter-05",
      "provenance": [],
      "collapsed_sections": [
        "Xza3nUtpqlU_",
        "pOLW04W-OYME",
        "KX5nxDGRVOww",
        "0LC74rWE18OP",
        "wjhjZ-p42RNT",
        "Z6JNob1u_B6Y",
        "4NDeTK9oBAn1"
      ],
      "toc_visible": true,
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "accelerator": "GPU"
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/jo-cho/advances_in_financial_machine_learning/blob/master/Chapter_05.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Xza3nUtpqlU_",
        "colab_type": "text"
      },
      "source": [
        "# Intro"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "B-mMhkzOsCoe",
        "colab_type": "text"
      },
      "source": [
        "Looking at the sequence of weights, $\\omega$, we can appreciate that for $k$ = $0,…,∞$, with $\\omega_0$ = 1, the weights can be generated iteratively as:"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "7zQzeAE6swol",
        "colab_type": "text"
      },
      "source": [
        "$$ \\omega_k = −\\omega_{k−1} \\frac{d − k + 1}{k} $$"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "dhjwV6t5udiV",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "import numpy as np\n",
        "import pandas as pd\n",
        "import matplotlib.pyplot as plt\n",
        "import seaborn as sns; sns.set()"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "k1evtkOeqrHc",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def getWeights(d, size):\n",
        "  # thres>0 drops insignificant weights\n",
        "  w = [1.0]\n",
        "  for k in range(1, size):\n",
        "    w_ = -w[-1] / k * (d - k + 1)\n",
        "    w.append(w_)\n",
        "  w = np.array(w[::-1]).reshape(-1, 1)\n",
        "  return w"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ptFOBsLpsVVp",
        "colab_type": "text"
      },
      "source": [
        "the sequence of weights used to compute each value of the fractionally\n",
        "differentiated series."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "hxDW55kBq4Q4",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def plotWeights(dRange, nPlots, size):\n",
        "  w = pd.DataFrame()\n",
        "  for d in np.linspace(dRange[0], dRange[1], nPlots):\n",
        "    w_ = getWeights(d, size=size)\n",
        "    w_ = pd.DataFrame(w_, index=range(w_.shape[0])[::-1], columns=[d])\n",
        "    w = w.join(w_, how=\"outer\")\n",
        "  ax = w.plot()\n",
        "  ax.legend(loc=\"upper left\"); plt.show()\n",
        "  return"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ozJ2CYg2rDWZ",
        "colab_type": "code",
        "outputId": "161af9f2-788f-44f3-80d2-415e2a63f857",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        }
      },
      "source": [
        "if __name__ == \"__main__\":\n",
        "  plotWeights(dRange=[0, 1], nPlots=5, size=6)\n",
        "  plotWeights(dRange=[1, 2], nPlots=5, size=6)"
      ],
      "execution_count": 4,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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Oqo4QAl1TiMUNDMNEU3vnYuziiy/jO9+5Hk3T+OCD97nzzh/x3HMvJIdSlSRJ6k0nVLCY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\nSpKFEEIIq/4/RL5dUmUoFGEAAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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/w+14gvUcri7gYPVRtpbuYlPJNmIUG8MS88hPvny/g1AUEu66G+eEiVT//S1q\nVyynYfs2khc9xJzPDeODd47w3hsHmPdQPjZjGLTBDabXCULspMkXfYrXdZ2aKh8mWcfirSacGEet\n3kSaLRHZU4GIiSNkiqWipok4p4U4h+W627tly4ekpqYxcOCFoYn33Xc/X/7yV1EUhT17dvH009/l\nr39dSlxczxxJ1B5N3hDlJR7GTMpqCb3omoZn0wasuQOxfibz6ydVBznbWMqX8hZhkrvu6dlliWNK\n5gSmZE4gEAlS8Kn5Dnsqm/sd4nNbQksX63cwxceT/vjXiZs2g6o3Xqf8v14hJm8YM2fcx/oPK1j+\nxgHufWgkMdfYn2Vg0BF6nSBcCiFE85yEMBZJwhKIIKzgVQO4LHZ0fyMWmwubRaHeF8IZY77uuexX\nrXqPe+65t9W2m2GthOJj7jbhoqYjhwm7q0hc8LlWZSNahBXFa8iwp3FrWuevwX21WBVL+/0O1UdZ\nciza79DP2Yf8pGHkJ7ff7xAzaDBZP3wez+ZN1Lz7DtqrP2fypHvY4U7mvfOi4DBEweDGcFMJAkQn\nqfmbwqhWJzQ1EmOPdi7HWRMg6EMPenE57JTX+GhoCuG6jl5CVVUlBw/u4/nnf9Jq+82wVkJxgZuE\nZDsJSRfCRZ6N65Hj4nCOGduq7LbS3VQHavnGyK9c0xyB68nF+h0OVR9l5akPWHmqud8haSj5ya37\nHYQsE3/7TJy3jqP6nb/TsG0FoxIHsF+7jeVv7Ofeh0Zid15/b9XA4KYTBJNZjvYTyGZkXcMRkfGh\n40fFZrKgN9VjTnBisyg0NHsJcge9hCtZDwFg9eqVTJ48ldjY1nlvevtaCd7GIOXn6rl1av+WbaHK\nSnyHD5E4bz5CufC19EcCrD69nkGuHIYmDG5Tlx7w0njoEyIRM8KegORIQJg6N2dRR/lsv0N9sKEl\nz9LWsl1sOne+32EI+cnDWvodFGcsaV/+Cq7bplP1xuuMPLuK/dps3n1tL/O/OBZHrCEKBteXXr0e\nwsVorA8Q8IdxRuqRFIUaByAEqYoDvaEKEZtCWLJSXu3D5bDg6oZPZz15PYQDe86xY0MxDz1xK66E\n6Ggh91tvUrdxPQNe+hWK60JfyYqTH7Dm9Aa+P/ZbZMW2XpBG1yI0Lf8pmvtk6xNY7FFhsCcgORIR\njvOviUj2BITdhZC65lkoEAlSWHucg839Dr5IU0u/w4hm78FliUPXNBp2bKfovfV87JqC1SSY//AY\n4tITLlm/sQbABYxrEaUj6yHcdB4CfDps5ABvHY64BGrDjYQtCopsinoJrhhirAr1TSGcdhOy1D1D\nFT2R4oIqklIcLWKgBYPUb8tiN6kAACAASURBVN+K85axrcSgPtjAxrNbGJOS30YMAEJ730VznyTp\nnn/AJ7nQfbVo3hp0b/Orr5ZwZREEfa0PFAIR47ogEI5PCYc9+iqszuuS/daqWBiVMoJRLf0OZ6J5\nlqqP8tbxZbx1/Hy/w1DyRw1j5Ogx2Je+z9ZSF+/8aRezbrWROWtamwl7BgadwU0pCCazHB2CKkzI\ngDWoIckCb9hHvC0W3VsDkSAuh4Wmah8NvjDx3dBL6Ik01geoLGtk/LTslm0Nu3ZGVyCb0XqJzPdP\nrSOiq8wbMKdNPZHSo4T2r8I05DZiR80keIknQT0cQPPWtisYas0Z9DP7QA23Pkg2NQtEQlQ4HAmf\nEpDETglNRfsdBjAwfgCfy51LRVMVB91RcVh5ai0rT60l0RpP/qRhjHLb2L9VYt1HTUzY/RL9v7AQ\nW07bGfAGBtfCTSkILaONmsJYLFY0n4+YhBiaIn5c9lTw1UW9hLhUYqwmGnwhYg0voVMoLnQDF0YX\n6bqOZ+N6LH37Yc29cIOr9FWxo3wPUzMnkBLTuv9ECzQS2PTfSK40LBO/cNlzCpMVOT4D4jPa3a/r\nOnqgsa1geGvRfLVopUeINHlok1XxYqGp8587EJoSQpBuTyXdnsrs5n6Hw+fzLJXtYpMWIS4/iazD\nt7AzPIrgv/+GtFvzSbp/IUovGo5s0LXclIIAYLUq+H1hNKsDqb4aB2a8ehNNkQB2Wyx6kwc9Esbl\nMNMUCFPvC5Hg7NrOyt5AUYGb5DQnsa5o5k//ieOESs+R+uVHW4Volp9cg0lSuKt/a69B13WCm/8H\nPeDFNucfEaZr99yEEAhbLNhikZP6t1tG1yLoPg+arxbdWxP1OM6/+mouHZq6mGBcIjQVZ4llcuZ4\nJmeOj/Y71J3goPsIx6VPSD08kl1ZdzPu4zV49n6Ec+49ZNw5t1VnvIHB1XDTfoMUUzRsFNIlrEIg\nNQWxWE00hrw4bEnoTfXo/nrMziTsNhONvjBxMWZk2fASrpYGjx93RSMTZ1xYZtKzcT1SjB3nuAkt\n207Wn+aA+zD3ZM/CaW7dGRY+upHImX1YJj6EnHTjOtKFpCCcSUjOi4/20sNBNN9nPIxmwVBrzl48\nNHV+dNRFQlNWk5VRycMZlTwcdYjKwYEn2P1eObuy76Ffw1oGvfMuH29ag/euyQybMYuAV8MsmzBL\nJkyyCbNkxiQpxoqABpflphUEIUTUS2gKY7PFoPp8OBwJ1AQ9BHUVs9WBHvCi2+OJc5jx+Zu9hFjD\nS7haigqi4aKcIdFwUbiuDu8nHxM/604kS/RJX9d13i16H6fZwe19b2t1vFp7juCuJch98zEN71jq\n6xuBMFmQXRngukRoKuht9izaC00dJdJU135o6lOd30MdCWTeFs/7WxWqEu/FPKaE5C1byHhjA4fX\nbcFvlQjLEJEFEUVEX2WBbpLBZEI3KWAyI5kUsJiRTGYkswXZYkE2m5EsVhSzFcVixaxYMMvmT4mL\nKfpZNmGSzIbw9DI6TRBOnTrF008/jcfjweVy8dJLL9G/f/9WZVRV5cUXX2Tr1q0IIXjiiSdYuHBh\nZ5nQYSxWE02+MKrFjtTkwxoBSQi8YS+JtthoXNnfiNnuinoJzamxlct4CfX1Hn7842cpLT2HyWSi\nT59+/PM//yvx8fGtygUCAX760xc4dqwAWZZ58snvMLmdDJ+9heICN6kZTpxxUVGt37wJdJ246ReW\nyDxUfZTi+tM8OHgBVuVCOEiPhAhs+C+E2YZ1+mM98qYjhEBYnWB1Xjo01VTfVjA+M2rKBsy0xLG+\nYQ7njiUyZGgKep2X9OoAeoMGEQ1UPZqzS9UR2tWNLo9IrYXFK9NKZCKKuCA+skBVBJoio5tMYFLA\nrCAUE5jNSC1/lhYBUixWZIsVk9mK2WQ1hKeL6TRBeO6551i8eDHz589n+fLlPPvss7z22mutyqxY\nsYKzZ8+ydu1aPB4P9913HxMnTqRPnz6dZUaHUEwSsiwIqQKrLKP5fNhj7XhDXuItLjDb0P0N6DGx\nuD7lJSRexksQQrB48ZcY0zzj9ve//w1/+MPv+MEPnm1V7s03/4Ldbuett96lpOQsTz75OEuWLCMm\n5vpl8uwqPLVNVFd5mXRHDgBaOEz95g+x54/E3DwrW9VUlhevJiUmiUnp41odH9y1BK2uFNvd30Oy\nxbapv7cgJKU5VJR40TLnQ1M2by33VNTw/laN9Z4Z3Jl9lOyBbiKhMLoWAU0FNfqqqWH0iIoeiaCr\noGuAFn292J+mgaqBqutomo6mCTQ9ul2PRI9v+VN1hAZCBekqZzZFJFBlQVgRBGTwfkp0LrxC+LzH\no0joioyuSKDIUQFSFCSzCWEyYbKaUVUQkhT9ExJCEiAkhCQjSRJIAiFFU+MLZIQsIYnoqxAyQpKQ\nFAWEjCQkJEVuOVaSlOh7WUaS5OhxQkRfJQkJqXm7iL4XAiGkaD3N28T590JCovV+QfN2IUXr5UJZ\n0Vz+/L7OolMEoaamhqNHj/K///u/AMydO5cf//jH1NbWkpBwYSLN+++/z8KFC5EkiYSEBGbOnMma\nNWt47LHHOsOMDhMdbWTC3xQiJsaB5m3AER9HI1584Sactji0UAV6wIfJ5sQRE/US4i7jJcTGxrWI\nAcCwYcNZtuztNuU2bFjHM888D0Dfvv0YMiSPXbt2cPvtM9uU7ekUnw8XDY6Gi7yf7EVtbMD1qbbu\nqthLRVMVjw3/Yqt00uHTnxA+uhFT/hyUPsNb1avrOjX1fmrqAzegFd0IkQDOBCRnLtNTAnz4XgEf\nlIxi9sJ8NC5zR9aa7+KaClok+llTiSqFilCbFUOPIDQN5by4aBrQvP9T5aP7ovuFFol6OeEwRM6/\nNovR+W2RaHk9HEFXNTQ1gqZG1UeoGoqmIWkaJlVvNkNHD+kIFdBpFp6oAEm6CqhA+JJNvt7ogC6a\n9VFEP2tCgABEdFv0VUT/O81loymVBZp0oY5Wf+frF6LN9uj76Dn0Fk0QLe91AQiBIzGRRc/9/Ira\n0SmCUF5eTmpqKrIc/RHLskxKSgrl5eWtBKG8vJyMjAvx1fT0dCoqKjrDhBaOHaqg8OCV16npOpGw\nhiwLRDiEMNUQFhq6XoZZNkMkCFSBYmHQ8FRiUu3Ue0Mkxl1ZX4KmaSxb9jZTptzWZl9lZQWpqRcW\nkE9JSaOqqnOvR3ehqNBNWp/YlvQLng3rMaWmEZMXTeMRUkOsOrmO7Nh+jEq+cNPXfHUENv8JKSkL\ny62fb1VnRNX47xVH2VtYdeMa0k0xA0OQWPH6vht0Rrn5r5MQRO9GN22v5vUjTrZdcdked/nbm4Jd\nVSWhNC9SLskdc6FkIVCFhq5HXUtdVVHMCiE1jI6OJJvQIyGErmEyycTazTT4wiTGWVvOeSl++cuX\nsNtjWLTowaiL+imEiKagaLFdEkiSdEX1Ap86TiI52XnFbb7RuCsaqXX7mLNgGMnJThpPFBE4WUz2\nY18hJTWaHnrZ0TXUhxr4pymPkZIcDQnpmkr5B/+O0FQyPv89zIkX+mDCEY1f/GUPewuruH9GLpnJ\nVzY1vzcTCoTxlHvbdkob3NTYO5BCvVMEIT09ncrKSlRVRZZlVFWlqqqK9PT0NuXKysrIz48u9vJZ\nj+FKaC+XkaZpLXl9Bg5NYeDQlA7V6W0M0uQN4YrR0OpqMWVkUB6swSKbSbIlotWeA1lBdqUQiWg0\n+EJU1wdIuoyX8MorL3P27Fleeuk/ol65prXan5KSRmlpKU5n9KZYUVHOqFG3tLTlUnw6l5Gmad06\nZ8ueHacBSM2Mxe1upOKdFQiLBSl/LG53I96Qj2VHP2BEUh5JpLW0JbhvJaEzh7FO+yr1mhOat4cj\nGv/17mH2F1XzhVmDeHBOXrdu/40keVqucS2aMXIZRelICv9OGVSfmJhIXl4eK1euBGDlypXk5eW1\nChcBzJkzh6VLl6JpGrW1taxfv57Zs2d3hgnXhLV5YfOIbAEEmteH3RSDPxJA1dXopKVwAD0cRFEk\nnDYzXn+I8CVu3Oczlv7sZ7+66NKYM2bcwfLl7wBQUnKWgoKjTJgwsd2yPRVd1ykqdJPRL44Yhxm1\nsZHGj3YRO3EycnPn+ZozGwiqQe4dcFfLcWpVMaG976AMGIcyaErL9nBE5ZV3DrG/qJovzh7MHbd0\nzYAEA4PeSKfNsnr++ed5/fXXmT17Nq+//jovvPACAI8//jiHDh0CYP78+fTp04c777yTBx54gCef\nfJK+fdsmLbvRyIqErEiEghqSzYbq8+Iw2dEBX7gpOlRQSOj+egDiHGZAUO8LtlvfyZPF/OUv/0t1\ntZuvf/0rPPLIYn7wg+8B8Mgji6mujnawLl78JRobG1m06D6+//3v8P3v/ysxMfZ26+yp1Lp9eGqa\nyM2Lem3127agRyK4ZkSXyKz217Ll3E4mpI8lw5EGgB7y49/wB4Q9HuvUL7eEAENhld++fYjDJ2t4\n5K4hzBid2TWNMjDopXRaH0JOTg5Lly5ts/3VV19teS/LcotQdCfOT1LzeUPYnXbwNyGFIlgVC96w\nj1izE2F1RoegqmEU2YQzxkSjL0Sc3YxJad25NmBADtu27W33XH/+8xst7202Gy+++NJ1bVtXU1Tg\nRggYMDipeYnMjdiG5GHJjN7MV578AEkI7sme1XJMYNtr6N4aYub9AGGJCmQwrPLbvx+k8Ewdj96d\nx5T89HbPZ2BgcPUYeRiasTSHjcLCBJKE6vXiNNmJaCr+SCAaNgJ0fwMAcXYzQgg83lCX2dzd0XWd\n4kI3mVkubDFmfAf2E6mtaRlqWtJYyp7KfczoO5V4azRBW/j4diJFOzHfMh85bSAAwZDKb5YeoPBs\nHY/NHWqIgYHBdcIQhGYUk4yiSAQDKrLdjtbkwypZkIWEN+xDyArCYo+ms9BUFFnCGWPC5w8Tjqhd\nbX63pLrSS32dn5zmcJFn4waUhAQcI0cBsLx4NXYlhln9pgOg1VcS2P4X5PTBmEfNA8AfjPAff9vP\nsRIPj88bysThaV3SFgODmwFDED6FxaYQDqlgc4CuozU14TDbCUQCRLRI1EvQNfSAFzC8hMtRVOBG\nkgQDBiURLCujqeAIrum3I2SZwtoTFNQeZ3b/24kx2dDVCP6NfwBJxjrjCYQkNYvBAYpKG/javcOY\nMNQQAwOD60mvEYTOWAm0JWykSwiTCa25cxnAG/JFUy2brNG+BF1HliWc9qiXEAp3jZeg6xrN0x27\nFefDRX36x2O1mfBs2oBQFGKn3oama7xbtIoEazy39ZkEQGjvO2juU1hvexTJkUhTIMKv3trPqfIG\nvj5/GOPyUru4RQYGvZ9eIQiKYsbna7hmUVAUGcUkEfSHke0OtEAASdWxKla8YR+6riPZ4kCLoDfn\nvo+LafYSfDfWS9B1nUgkjMdTjdnc/TKwVpU30lgfIGdIMqrfT8OO7ThvHY/ijOXjygOUeMuYN2A2\nJkmJrn52YDWmIdMxZY/FFwjzq7f2caaikW/cN5yxQzo2r8TAwODq6HEzldsjPj6Zujo3Xq/nmusK\nBiKEgipNdgXN50EqCaBaouskqA1NmCUTelMDNDREFz8REAlEqKqPEPJZUOQb87QenfUssNkcOBxx\nN+ScHaG4wI0kC7IHJdGw40P0YADX7XcQ1iKsOLmGTEc6Y1NHofkbmlc/S8cy6SG8/jC/WrKf0mov\nT35uBKNyL77+gIGBQefSKwRBlhWSkjpn5EmDx89f//ARE2YMIGnrOkK1tfR78ae8sOsXJNoS+fbo\nJwgXniGw5X+w3f3PKH2G4fWH+Zc/7GBo/wSeXDCiU+y4HN15Fub5yWh9sxMwW2TKNq7Hmj0Aa/YA\nNpVsoyZQx5Mjv4pA4D+/+tld/4Q3JPjVkn2U1TTxzc/lk59z8YyfBgYGnU+vCBl1JrEuG8lpTooL\n3MROnES4qpLQyZNMzhjP8boiKn1VKAMnImyxhA6tAcBhMzFrbF8+PubmbGX3vEnfSCpLG/A1Bskd\nkkxTwVHCFRW4br8Df8TP6tPrGRyfS17CIMJHNqCe3Y9lwiJ8tjR++eY+ymubeOrzIwwxMDDoAgxB\naIfcvGTcFY1oOcMRZjMNO7YzMeNWJCGxrWw3QjZhGjYTteQQau05AO68tS8xFoXl2051sfVdT1GB\nG1kW9B+YiGfjemSnE8fYcaw7sxlfuIn7cu5Gqz1HcPcS5H4j8fe/jV++sY+qOj/f/nw+w7MNMTAw\n6AoMQWiH80s8njrViGPMLTTu2Y1DWBiVPJxd5XsJqWHMQ28HxUzoYNRLiLGamD2uL/tOVHO6oqEr\nze9SNE2n+JibfjmJiMY6fAf2E3fbdBq0JjaWbOWWlJH0jUkmsPG/EGY7obFf5Bdv7sNd7+c7C0cy\ntH/C5U9iYGBwXTAEoR2ccVZSM5rDRpOmoPn9+PbvZ2rmBJoifvZVHURYHZgGTyVStBOtKdqZPXNs\nX+xWhXe33rxeQsW5epq8IXLzkvF8uAmEIG7adN4/tQ5N17g3Zw7BnUvQ6sqIjH+El94porYhyD89\nMIohWfGXP4GBgcF1wxCEi5CTl0J1lZdQShZKfAINO7cz0JVDSkwSW0t3AWAeMRs0jfDh9QDYLApz\nxvfjYHENxWX1XWl+l1FU6EZRJPr2dVK/dTOO0WOosUTYUbaHqZkTiKs4TbhgE+qQWfx8Y4B6b5B/\nWjSSQX1dXW26gcFNjyEIF+F82Kj4WA3OCRPxHT6E2tDA1IwJnGo4w7nGMqTYFJTsWwgd3Ygeji7h\neMctfXDGmG5KL0HTdE4WusnKTSSwfy+az4drxh0sL16DRTZzZ/ItBLb8D1p8Fj8/0o9Gf4jvLhrF\nwD6GGBgYdAcMQbgIDqeF9D5xFBVUETtxMmgajbt3Mj59LIqksK1sNwDm/DkQaiJ8bCsAVrPCXeOz\nOHKqluMl1z4voidRdtaDvylMzpAkPBvXY87IpCzVysHqI8zsexumbX9BVyP8p3sC3oDO9x4cTU5m\n95tDYWBws2IIwiXIyUumrroJnykOS/9sGnZux26K4ZaUkXxU8TGBSAA5NRcpNZfQobXozSuizRiT\nSazdfNONOCoudKOYJFKEh+DZM8TNuIPlJ98nzuxkcp0XtfwYy4MTKAvZ+eeHRpOdHtvVJhsYGHwK\nQxAuQc7gZISIxsXjJk0mWFJCsOQsUzInEFRD7K3cD4A5/y70RjeR0x8DYDHJ3DMhi4IzdRSeqevK\nJtwwVFXj5DE3/Qcm4d2yEclm4+xAFyfrzzAncRR8soJDWg57Qjn880OjyUrrvmtAGxjcrBiCcAli\nHGbS+7ooLqjCcet4kGUadmwnO7YfmY50tpXuQtd1lKzRiNgUQgdWt+RTmjYqA5fDzLvbTnVK4r3u\nTukZDwF/hOx+MTTu3YNz0mSWn9tIqi2R4R9/iEeL4d3QJL7/0Bj6pRpiYGDQHTEE4TLk5iXjqfXj\naRI48kfRsHsnaBpTMiZQ4i3jTGMJQpIwj5iN5j6JWnkCALNJ5p6J/Tle4qHgJvASigvcmC0ysWf2\ng6pyamgylU1V3F4vkHy1LA1N59sPjadPiqOrTTUwMLgIhiBchgGDkxAiGh+PnTQZtaEB35FD3Jo2\nGrNsbhmCaho8BWFxEG6eqAZw28gM4p0W3t3au70EVdU4ebya/jkJNG7dhHXYMN5r/Ig+sov8s0f5\nUB3DQw/dRWayIQYGBt0ZQxAugy3GTGZWPEUFVcQMH4HkcNCwYwc2xcqtqaP5uPIATeEmhGLBNHQG\nkdP70DwVAJgUiXmT+lNUWs+RU7Vd3JLrx7lTdYSCETLM9ageD6eGp1AfamT26bOc1tIY/8AjZCTZ\nu9pMAwODy2AIwhWQm5dMgydATU2A2HET8O3/BNXnY2rmBMJamN0VnwBgGjYTJJnQoQ9ajp2Sn05i\nrJVlvdhLKCpwY7YoxOz/EDkpieXycbIbdfoEdNLmfZP0JKPPwMCgJ2AIwhWQPSgJSRIUNaey0CMR\nGvfuoa8zk/6x/Vo6l6WYOEyDJhE+vg3NH81npMgS8yb351R5AweLa7q4JZ1PJKJxuqiarEwrwaJj\nFA1OJqiHua+2FmnyI6Rk9ulqEw0MDK4QQxCuAKvNRJ/+8RQXujH364c5I4OGHdsAmJI5gYqmKoo8\n0TkHphFzQA0TPrqp5fhJw9NIdll7ZV9CyclaQkGVFM8JdMXEBynV3NrgJ6nvJJKGT+xq8wwMDDqA\nIQhXSE5eMo31AdwVXmInTiFQXESosoJbUvKxKTa2lu4EQI7PQO43kvCR9eiR6LKaiixx7+RszlQ2\nsv9EdVc2o9MpKnRjsSqY923kaJoD1QJ3hO3ETX+4q00zMDDoINcsCH6/n+985zvMmjWLOXPmsGnT\npnbL7d69m5EjRzJ//nzmz5/PwoULr/XUN5TsgUlIsmhOZTERhKBh5w7MspkJabew332YxpAXiKaz\n0AONhE/saDl+wrBUUuNtvLvtFFov8RLCYZXTJ6pJNHmRwiH2j4Ap9QEy7ngSoVi62jwDA4MOcs2C\n8Kc//QmHw8G6dev4wx/+wDPPPIPP52u3bE5ODsuXL2f58uUsXbr0Wk99Q7FYFfpmJ1BcWI0c5yJm\n6DAadm5H1zSmZI5H1VV2lu8BQE4fgpSURfjgGnQ9ms5CliTunZJNSZWXT465u7IpncbZ4loiYQ17\n0UdUJlpoipW5c+BdyIl9u9o0AwODq+CaBWH16tUsWrQIgP79+zN8+HC2bNlyzYZ1R3LzkvE1Bqko\nbSB20mQiNTX4TxwnzZ7KQNcAtpXuRtM1hBCY8+9Cq69APXuw5fjxeamkJ8awfNspNK3newn7Pi5F\n01X6NJ7k4yEWZuouYkfc1dVmGRgYXCXXLAhlZWVkZma2fE5PT6eioqLdsqdPn2bBggUsXLiQZcuW\nXeupbzj9cxORZUFxgRvHqDFIVisNO7YD0c7lmkAthbXRmcrKgLEIewKhg6tbjpckwfwp2ZRW+9hT\nWNUlbegsDp5wU1niITFQRtAqqEk3M33yNxBCdLVpBgYGV4lyuQILFiygrKys3X07duxod3t7DBs2\njM2bN+N0OikpKeHRRx8lNTWVSZMmXbm1QGJi1852HTg0lVMnqpn/4CgapkyietsOEp76OjMTJvB2\n0Xt8VL2XaUPGAuCZOI/a9f9HbLgSS0YuAHclOli9+ywrd57hrqk5yNLV30CTk7tmfP8nhVW8sewI\nWQiyaw6xf6CNhUNm0ad/VpfYA113LbojxrW4gHEtOsZlBeFyT/IZGRmUlpaSkBBdC7e8vJzx48e3\nKedwXLiR9+3bl5kzZ/LJJ590WBBqarxdGm7pOyCewkMVHNp3DteY8WjrN3J63WZiJ0xifOpYNpRs\n4XhJCfFWF3qfCWD6G5Vb3sF2xz+01DF3Yha/X3aYVZuLmDg87arsSE524nY3dlazrpiDxdW88s4h\n8kwKllAAZ7CK6kGZDM+a1SX2QNddi+6IcS0uYFyLKJIkrvhB+ppDRnPmzOGtt94CoiGhQ4cOMXXq\n1DblqqqqWsbgezwetm/fzpAhQ6719DecrJxEFEWiqMCNLXcgSlLSp8JG49F0jR3NncvCbMOUN43I\nyT1ojReGm44elEy/FAfLt59CbV5DoSew/0Q1v3v7EH0S7cSEdZLqiyjuZ+ausV9AEsYIZgODns41\n/4q/+tWv0tDQwKxZs/ja177Gj370oxZv4De/+Q1vvvkmAGvXrmXu3LnMnz+fhx9+mPnz5zNz5sxr\nPf0Nx2SWycpNpPiYGx1B7MTJNBUcJVxXR5ItkbyEQewo+whVUwEwD58FCEKH17XUIQnB/KnZVNX5\n2Xm4sota0jE+Pubm98sO0S/VyYJRGWiaTlrDKTyjshmanNfV5hkYGHQClw0ZXY6YmBh++9vftrvv\n29/+dsv7hx9+mIcf7h2TlXKGJFNc6KbsrIeUCZOoXbGcxl07SLjrHqZmTuC/D73G4ZpCRiYPQ3Ik\nouSMI1y4GcuYexGWaJK3UblJZKU5eW/7KSYMS0WRu+8T9t7CKv743hH6pzn5xwdGsfH1TZjVMEFb\nLdOmPdXV5hkYGHQS3fcu1I3JyknAZJajSd1SU7HmDqRhx3Z0XWd4Yh5x5li2NafFhuZ1l8MBQgWb\nW7YJIVgwNZvq+gA7Drc/Kqs78FFBJX9YfoTsjFj+adEoqCzmXLVMWsMpGsYOpl+skavIwKC3YAjC\nVaCYZPrnJnLymBtV1YidNJlQeRnBM6eRJZnJGeMoqD1OtT+azE5OykLOHEr4yDp0NdJSz4gBiQzI\niGXF9lNE1O7Xl7DzSAV/fO8IuX3i+KcHRmIlyIkPVqMj4wqeZtycL3a1iQYGBp2IIQhXSc6QZIKB\nCKVnPDjH3opQlJaEd5MyxiGEYHvZRy3lzSPmoPvqiBTvbtkmhOC+qdnUNATZerD8hrfhUmw/VM7/\nW3GUwX1d/OPCkVhMMoGt/8ex/9/enUdHdeUHHv++2lRaqrSWhDa0giRWsQtJYCNkFluAmD5uO4y7\npxNPdyee7vZxTs5J+nT+SJzkJN1/xOGc9nR30p52Zux4Op4+BowxYCP2RcjsGLFoQ0IL2lXaan1v\n/igoURa7hEqC3+cv6dZ97916kuqn+7vv3muPx+zuR50VjS3y8Z6QEkJMThIQHtP0zBhMIXpqqzvQ\nh4UTsWAh9pOVaB4P0eYo5sbmcazlJB7V1yPQp85FF52E6/zugBVPZ6fHkJ0Syc5jDbg93mC9nQCH\nz7Xwvz6rJi89mjdfnk+ISY/n6hEGa87R5UkkfqCBuRuejvEgIcQICQiPSW/QkT4jjrqrnXi9Kpbl\nRagDAwxeOAf4Zi4PuAc513ER8PUGTHPXoXY34W2+5D+PoihsLs6gp9/JoXPB7yUcONvM7z6/zOyM\nGH7yrXmEGPWovW04jn7A2dBFgI7ImEGiEqcHu6lCiHEmAWEMsnNtuJwemup7CJ89B31kJH235iTk\nxswg1hzj33MZwDBj3XIAIgAAIABJREFUOUqoNWA5C4DctGhyUqPYebwBlzt4vYT9p2/wv3dfYV5W\nLD/+1lxMRj2a181wxa/Q9Abqu+MIddmZs35N0NoohHhyJCCMQUpGNCFmA7XVHSh6PdZlyxk8fw5v\nfz86RUdx8jKu9dbRNuiba6DojRjnvID3xkW83Tf857k9ltA34OLAmeagvJcvv2ri/+y9Sn52HP9j\n81yMBj0Azqo/oHZe5+u5a/E4orGprUTOmR+UNgohniwJCGOg1+vImBlH/bVOPB4V6/Ii8HqxV/kG\njpcnLkGv6DnSPDKQbMpbBQYTrvO7A86VMz2aWenR7DpxHadrYnsJe0828h9fXmPBjDje2DwHo8H3\na+FpuoD7/G50eas4deEmKDryFmag6OTXRoinkfxlj1F2ng23y0tTXTchqamEpE73L2VhMUWQb5vD\nibZTuLy+3dMUcwTGnBV4ao6jDvYEnKu8OBP7kJuKMzdGXedJ+bzyOv+3oobFOTb+rHyOf4KcOmzH\nceDf0EUnczoti9CWSMLcfUwvLZqwtgkhJpYEhDFKmh6FOdRAzWXfpjfW5UU4G+pxtvhSPyuSCxj2\nDHOqfWRfBNPctaCpuL/eF3Cu7JRI5mTG8PmJRoadHp60z4438PH+WpbmxfPDTbP9wUDTVBwHfovm\nGkJ5/nX2f30IF/FMj9EwhIU98XYJIYJDAsIY6fU6MnNsNFzrxO32YllWADqdv5eQHZVJQlh8wMxl\nnTUeQ/oiXJcq0NyOgPOVF2cyMOym4vST7SXsOFrPHw7WUTA7ge9vmIX+jjSQ++IXeJvOE1LwKgcH\n6kisDgVFIW/VvCfaJiFEcElAGAdZuTY8bpXG2m4MkZGEz5lLf+VxNNW3e9qK5AIa7I009Y8MGJvm\nrQPXEO4rhwPOlZlkZX5WLLsrn0wvQdM0th2uY9vhegrnTOO/vxQYDLyd13FWfowhbQGO7GV82bCf\nsIEULAwxbVbGuLdHCDF5SEAYB0nTowgNM1JT7dsFzVpYhKenh6Fq33yDZdMWYtQZAnoJ+oRsdAnZ\nuC7sRVMDB5HLV2Qy6PDwxVdN49pOTdP45HAdO442UDwvkT95MQ/dHRv0aG4njn2/QjFHEPLcn7D7\negUpDV7spngys6PGtS1CiMlHAsI40OkUMnNtNNZ243Z5CZ+fjy4szJ82CjOGsSg+n6qbZ3B4RlJE\npnnr0fo78DScCjhf2jQLC2bEsedkE0MO97i0UdM0/t/BWnYeu87K+Ul8b31uQDAAcB7/ELXvJuZV\nP6BLdXGk+QQzmlMByHtu7ri0QwgxeUlAGCfZuTY8HpWGmi50RhOWJUsZOHMK1TEM+GYuO70uqm6e\n8R9jSFuAYk3AdS5wOQuATcUZDDs97K0aey9B0zR+X1HD5ycaWbUgme+uy0H3jb2P3XVVuC8fwpT/\nIobkWXxat5u4Pi99nniizF6ibcHdulQI8eRJQBgniamRhEWYqPWnjYrRXC76v/oKgHRrKikRSRxu\nPuH/8Fd0Okxz16B21OG9eS3gfNMTLCzOsbG3qomB4cfvJWiaxkdfXmNvVROrF6Xw2pqZo4KBOtCF\n49Dv0NkyMS3ezHV7E6faz/H8jXjs5nhm5MsS10I8CyQgjBNFUcjKsdFY143L6cGcmYUxIQH78aP+\n14uTC2geaKXB3ug/zphTjBISgfvc56POubE4A6fLy56TjaNeexiqpvHBF1f58tQN1ixJZUvpDJRv\nBANN9eKo+A1oKqGr/xQUPdtqPydaC8V5w7d/0sz81Me6vhBiapGAMI6y82x4vRoN17pQFN/2msNX\nLuPu9M1RWJKQT4jeFLC+kWIIwTi7BM/1s6i9gRvlpNgiWJIXz5df3aB/yPVIbVE1jQ/2XGH/6WbW\nLZvOKyXZo4IBgOvMp3jbrmIu/i46azyXuq9ytaeGjT1J3DSnEBdjwhoV+hh3Qwgx1UhAGEcJyVYi\nrCEjTxstLwTAfvwYAGaDmSXTFnK6/RyD7iH/ccZZq0Gvx3Vhz6hzbirOwOXxsrvy4XsJqqbx759f\n5sDZFl5ansbLz2fdNRh42q7iOr0dQ/ZyjDMKUTWV7bW7iAuJJvxsG/1mGzPmS7pIiGeFBIRxpCgK\nWbk2mup7cDrcGGPjCM3JxX78mH/cYEVSAW7VQ2XbyJNFurBIjDMKcV89gjpsDzhnYmw4BbOmse/0\nDfoGH9xLUFWN3+2q5vD5VjYUpvNfVmbeNRhozkEcFb9BiYjDXPxdAKraztA80Eo5s2h2+gaRs3Jt\nj30/hBBTiwSEcZaVa0NVNeqv+rbPtBYW4W6/iaO2BoAUSxIZ1jSO3DG4DGCcuw68btyX9o8658ai\ndDwejc9PXL/vtb2qynufXeLohTbKizPYfK9goGk4Dr+PNthL6Oo/QzGF4va6+bRuD9MtycSfrqfd\nmk18YgSWSPNYbocQYgqRgDDO4hMtWCLN1Fz2pY0sixajmEz+wWXwrW90c6iDa711/jJ9dBL66fNx\nf/0lmiewJ5AQE0bhnGnsP9NMT7/zrtf1qir/9ukljn99k80rM9lYfO9Zxe4rh/DUVWFashl9fCYA\nB5uP0ePsZVN0IR3V9fQbo8ielfDY90EIMfVIQBhniqKQnWejuaEXx7AbnTmUiIWL6K86ier2fdAv\niJ9HmCGUw83HA441zVuH5ujHfe3YqPOWFaWjqhq77tJL8HhVfrPjEier23n5+Sw2FKbfs33e3hac\nxz5En5SHaf6LAAy5h9jTUEFezExiz9RxM8IXTCRdJMSzRQLCE3A7bVR3pRPwzUlQh4YYPHsWAJPe\nSEHiYs52XMTu6vcfp0/MRReXhvv8bjRNDThnfFQoRXMTOXi2mW77yGxnj1fl19u/5qvL7bxSks36\ngrR7tkvzunHs+zWK3oR51Q9QFN+Pf+/1Awx7HGxKLaXv8CE64vJITIkkwhIybvdECDH5jTkgbN++\nnQ0bNjBr1iw++OCD+9b9z//8T1544QVKS0t5++23UVX1vvWnqriECCKjQ6m9lTYKy83DEB0dkDYq\nTlqGqqkcb6nylymKgmneetS+NryN50adt6wwDU2Dz477egluj8r//OQip6928EelM1i79P77HDsr\nP0btasT8/OvowqMB6HH0cuDGEZZMW4C1uhG7x0i/aiYrT3oHQjxrxhwQ8vLyeOeddygrK7tvvaam\nJn75y1/y+9//nr1793L9+nV27Ngx1stPSoqikJVno/l6L0ODLhSdDktBIYMXL+Dp6wMgITyemVFZ\nHG2pRL2jN2DIXIwSETtqRzWAuMhQVs5P4tC5Fpo7Bnj3kwucrenkv74wkxcW33/ymKfxPO6LezHO\nWo0hbYG/fGf9XjRN46X0F+jd9yVdifNQFMjKkYAgxLNmzAFh5syZZGdno3vAtop79uyhtLSUmJgY\ndDodL7/8Mrt27Rrr5Set7FwbmsZI2mh5Eagq/ZUjk9KKkwvocvRQ3X3VX6boDJjmvIC39QrejvpR\n531peRqKAm+9c5DztV18d20Oqxfdf66AOtR7a/ezFEIKXvGXtwy0Udl6ipUphYS3dONoauSmJZPE\n1CjCIkxjvQVCiClmwsYQWltbSUpK8n+flJREa2vrRF1+wsXYwomKDfOnjUKSkghJz8B+/Ii/znzb\nbCzGiICZywDG3OfAGHrXXkKM1czzC5JxuDx8b30uzy9Ivm87/LufuR2YV/8ZimHkg3577eeYDSGs\nTS+ht2IfQ5Zp9Dt8g+JCiGeP4UEVNm/eTEtLy11fO3bsGHq9ftwbdT+xsVNn1c15i5I59MU1zCFG\nLFYznjWrqfvX3xI20EV4RjoAq7OL2H55L0q4m7iwmFtHWtAveoG+yp1Erfsexqj4gPP+6NsLePmF\nHJLiHnwvek/sYODGReLWfR9rTq6//FL7NS52VbNlXjnJ5hC+OlXFwJJvoXQrLClMJzxiag0o22yW\nYDdh0pB7MULuxaN5YED45JNPxuVCiYmJAYGlpaWFxMTERz5PV9cAqqo9uOIkkDg9EjSoOtrA3MXJ\nKLPyQa/n+md7sb3yRwAsiFrAdm0vn17YT1nmGv+xauZzUPkZbQc/wVy4ZdS5k2wWOjr6R5XfydvR\nwND+DzCkL8SRWojzVn1N03j/1P8jKiSSJdFLqNv2GarXy3VnFMnTIxgadjE0/GhrJwWT7SHuxbNC\n7sUIuRc+Op3y0P9IT1jKaO3atXz55Zd0d3ejqioff/wx69evn6jLB0VMXDgxtnD/JDV9RAQR8/Kx\nVx5H8/p2SYsLjSEvdibHWirx3rFzmi4iFkPWUtxXDqE5Bx/52prbwXDFr1BCrZhX/knAjOUzHRdo\nsDfyUsYajJpC74H9uGcV0N/vlnSREM+wMQeEnTt3snLlSnbv3s3WrVtZuXIlNTW+ZRq2bt3KRx99\nBEBqaipvvPEG3/72t1mzZg0pKSls3LhxrJef9LJzbbTdsDNg980wthYW4bXbGfz6or/OiqQC+lz9\nXOiqDjjWNG8duB24qg8+8nUdRz9E62v3zTcwj/x34FW9fFq7m8TwBAoSFzFw+hTevl66U/LR6RQy\nZsY95jsVQkx1D0wZPUhZWdk9Hzl98803A75/9dVXefXVV8d6ySklK8/GycMN1F7uYP7SFMLnzkMX\nEYH92FEi5s0HYHZsLlEhkRxpPkG+bY7/WH1cGvrkWbgv7sU0dw2K/uF+XO7aSjxXD2PKL8OQlBfw\n2tGWk7QPd/Kn876HTtHRu38fBpuNxi5ISY/GHGocvzcvhJhSZKbyExYVE0ZcQoQ/baQYDFiXFjB4\n9jTeQV8qSK/TU5S0lOruq3QMdQUcb5q3Dm2oF09t5UNdT+3vwHHofXTxmZgWlwe85vA42dXwBVmR\nGcyJzcPReJ3ha1dRl5bS3+eUyWhCPOMkIEyArFwb7S392Ht9S05YC4vQPB76vxqZpVyYtBSdouNo\nS+AHvz5lLrroZFznR++7/E2a6mW44jeARmjJn6LoAnsU+5oO0e8aYHP2iyiKQu/+fSgmE22haej0\nChkzJF0kxLNMAsIEuD1QW3vFt3NaSFo6pqQk7MdG5iREhUQyL24Wx1urcKsef7lvOYt1qN1NeJsv\n3fc6rtPbUW/WYF7x39BZAx9Vtbv62dd4kHzbXDIi0/AODNBfeQLLsuXU1faSmhFDiHnMGUQhxBQm\nAWECWKNCiU+0UHtrJzXf9prFOGprcN286a9XnFzAgHuQc+0XAo43ZBeghEbiOj963+XbPK1XcJ35\nFMOMIozZy0e9/nn9Ptyqh41Z6wDoO3oYzeXCNaeYwX6nPF0khJCAMFGycm10tA3Q1zMMgKVgOShK\nwIJ3OdHZxIXGcrglcOayojdinFOK98ZFvN1No86tOQZ8u59Z4jEXvTbq9fahDo60nKAwaSkJYTY0\nVaXvQAWhM3No7FbQ6xXSs2PH+R0LIaYaCQgT5PbeArWXfWkjY3Q0YbNmYz9+FO3Wqq86RUdx0jJq\neutpGWgLON6UtwoMJlznA/dd1jQNx6HfoQ31EVryQxRT6Khr76jbg0Fn4MX0FwAYvHged0cH1lUl\n1F7pYHpWLKYQSRcJ8ayTgDBBLJFmEpKt1NxKGwFYlxfi6epi+NrI4nYFiYsxKHqOfGNwWTFHYMxZ\ngafmOOpgj7/cffkgnoZTmJZ8y7/72Z0a7I2caT/P6tSVRIb4pvH37vsSfVQUA3HZDA24JF0khAAk\nIEyo7FwbXe2D9HQNARCxYBE6sxn7sZG0kcUUQX78XE62ncLpDVw+wjR3LWgq7q+/BMDb04zz2H+g\nT56Naf66UdfTNI1tNbuIMIZTOn0lAK62Noa+vkjUc6uovdqNwaAjLUvSRUIICQgTKvMbaSNdSAgR\ni5fQ/1UVqnNkr+QVycsZ9jg4dTNwkxydNR5D+iJcl/bjHer37X5mDMG86vv+3c/u9HXXZa711rE+\noxSzwQxA74F9oNdjKV5J3ZUO0rJjMZomdoFCIcTkJAFhAkVYQkhMifxG2qgIzelg4Mwpf1lWZDrT\nwhM48o1lseHWchauIVr+/aeo3U2Yn3sdXVjUqHqqprK99nPiQmMpTlrmK3M4sB89gmXxEtr7YHjI\nLfsmCyH8JCBMsOw8Gz2dQ3R3+GYph86YiSEuLiBtpCgKK5IKuN7fRKP9RsDx+oRs9AkzcHe3Ypxd\niiEt/67XOdl2mpbBNjZmrsNwa4Ka/cQx1OFhokpKqanuwGjSk5YVc9fjhRDPHgkIEywzx4ai4O8l\nKDod1oJChqov4e4ZGSxeOm0hRp2RIy2jewkhhVuwLlxLyLJv3/Uabq+bnXV7SbOksjB+HuAbT+it\n2EfI9DSMaRnUXekgPTsWg1HSRUIIHwkIEywswkRiahS1lzv8S1FYlxeBptF/4thIPWMoixPyqbp5\nlmHPcMA59LYM4tb/IGD3szsduHGUHmcv5dnr/cteD1+5jKulmaiSUloa+3A6PJIuEkIEkIAQBNl5\nNnq7h+lq96WNTAkJmLNn+OYk3LFe0YrkAlxeF1VtZx763IPuIfZc38+s2BxmRmf7y3v370MXEYFl\n6TJqqzswheiZninpIiHECAkIQZCZE+dLG10OHFx2tbTgvN7gL5tuSSHVkszh5hMPXNjutr3X9+Pw\nOCjPetFf5u7uYuDMaSKLV6LpDdRd7SR9Rhx6g/z4hRAj5BMhCELDTCSnRVNbPZI2sixZgmIwBCx4\nd3twuWWwjXr79Qeet9vRw4EbR1k6bSHJESPbk/Yd2A+aRtTzq2iq78Hl9JAt6SIhxDdIQAiS7Dwb\n9l4HnTcHANCHhROevxD7yUo0z8hqp4sS8jHrQzh8l0dQv2ln3V6AwL2Z3S76Dh0kfH4+xjgbtdUd\nhJgNpGREj/M7EkJMdRIQgiRjZhw6nRI4J6GwCHVggMELIxPSzIYQlk5byOn28wy47723cvNAKyfb\nTvNcSiEx5pEP+4GvqvAO9BNVUorHo1J/rZOMmXHo9fKjF0IEkk+FIDGHGklJD0wbhc+eg95qxX7s\nWEDd4uQCPKqHytZTdzsVANtrP8dsMLM2rSSgvLdiH8Zp0wjLm0VTXTdul1fWLhJC3JUEhCDKyrPR\nb3fS3toPgKLXY122nIHzZ/EODPjrJUckkhmZzpF7DC5f7anl667LrE1bRbgxzF8+XFeHo76OqJJS\nFEWh5nIH5lADSdNHz2wWQggJCEGUMSMOnf6baaNi8HqxnwwcM1iRXED7cCdXe2oDym8vYBcVEslz\nKUUBr/Xt34cSYsa6vAi320vDtU4yc2ySLhJC3JV8MgRRiNnA9IyYgElqIamphKSmBixlAbDANpdw\nQxiHm48HlJ9uP8/1/ibKMtdi0hv95Z5+O/1VlUQWFaEPDaWxthuPW5XJaEKIe5KAEGRZeTYG+120\n3bD7y6zLi3E21ONsafGXGfVGChIXc67za/qcvrpe1cuOut0khU9j2bSFAee1Hz6E5vEQtWo14Fsq\nIzTMKOkiIcQ9SUAIsvTsWPQGnX9JbADLsgLQ6QK21wQoSl6Gqqkcb60C4EhLJZ3DXWzKWo/ujuWv\nNa+X3gMVhOXNxpSYhNvlpbG2m8xcGzqdMjFvTAgx5Yw5IGzfvp0NGzYwa9YsPvjgg3vWq6ysZP78\n+WzatIlNmzbx8ssvj/XSTwVTiIHpmb60kar60kaGyEjC58yl/8Qx//aaAAlhNnKisznSXMmga4hd\n9V8wIyqT2bG5AeccOHsGT3c3USW+3kFDTRcejyqT0YQQ9zXmgJCXl8c777xDWVnZA+tmZWWxfft2\ntm/fzscffzzWSz81svNsDA26aG3q85dZC4vw9PQwVH0poG5xcgE9zl5+ceRXDLgHKc9+0b+A3W29\n+/dhiIklfL5vaeza6vZbi+pFPvk3I4SYssYcEGbOnEl2djY6nWSfHldaViwGY2DaKHx+PrqwsFFp\no/lxs7GaLFR31LAgfh7p1ukBrzubmxm+XE3UqhIUnQ6X00NjXTdZObZRgUMIIe5kmMiLNTQ0sHnz\nZgwGA1u2bGHz5s2PfI7Y2Ign0LLgmzkrgfprnWz+o3x0tx4L7V9RTMeBg0SHGzCEhfrrrpmxkm3V\ne/je4m9hs1gCzlP7h0MoRiOZ5S9itFo4f+oGXq/G4uVp2GyBdZ8mT/N7e1RyL0bIvXg0DwwImzdv\npuWOp13udOzYMfT6h9tgZfbs2Rw8eBCLxUJTUxN//Md/TEJCAoWFhY/U4K6uAX+u/WmSmhnNpXOt\nnDt9g5R039ITpoVLUffspWHPfiKLV/jrrrQVszqzCHXQQIej31/uHRriZsUBLEuW0etUoKOfM5WN\nRFhDCAk30NHRP+q6TwObzfLUvrdHJfdihNwLH51Oeeh/pB8YED755JMxNwggImKkQampqZSWlnL6\n9OlHDghPq+mZMRhNemqq2/0BwZyZhTEhAfvxowEBQa/TExtmoWMw8JfdfuwomtNJVEkpAE6Hm6b6\nHuYuSpZ0kRDigSYs8d/e3u6ffNXb28vRo0fJzc19wFHPDoNRT3p2LHVXOvF6fU8WKYqCdXkRw1cu\n4+7suO/xmqrSu38f5qxszOnpANRf7UJVNbJk7SIhxEMYc0DYuXMnK1euZPfu3WzdupWVK1dSU1MD\nwNatW/noo48A2Lt3L2VlZWzatInXXnuNTZs2UVpaOtbLP1Wy8mw4HR6ar/f6y6wFywGwnzh+r8MA\nfHsy32zzP2oKvg14LJFm4hMljyqEeLAxDyqXlZXd85HTN9980//1a6+9xmuvvTbWyz3VpmfEYArx\npY1ub29pjLMRmpOL/fhRYl7acM/UT+++L9BbrVgWLQHAMeymuaGX+UtTJF0khHgo8qzoJKI36Eif\nEUf91ZG0EfjmJLhv3sRRW3PX41wd7QxeOE/kyudRDL4YX3e105cuksloQoiHJAFhksnOs+Fyemmq\n7/GXWRYtRjGZRs1JuK3vQAUoCpHPrfKX1Va3ExkdSlzC0/mYrhBi/ElAmGRS0qMJMRuovWNJbJ05\nlIiFi+ivOonqdgXUV51O+g4fJmLhIozRvqeThgZdNF/vJStPJqMJIR6eBIRJRq/XkTEzjvprvvWH\nbrMuL0IdGmLw3NmA+v0nT6AODfofNQWou9KJpiFrFwkhHokEhEkoO8+G2+Wlqa7bXxaWNwtDdHTA\nPgmaptFbsQ9TcgqhM2b6y2svtxMVG0aMLXxC2y2EmNokIExCyWnRmEONATupKTodloJCBi9ewNPn\nWwTPUVODs6nRv0UmwOCAk5bGPrJzJV0khHg0EhAmIZ1OITMnjoaaLtxur7/curwIVJX+St/2mr37\nv0QXFuafqwBQd7kTQCajCSEemQSESSor14bHrdJYO5I2CklKIiQ9A/vxIzi7uuk/9RWRRSvQhYT4\n69RcbifGFk5MnKSLhBCPRgLCJJU0PYrQ8MC0EfjmJDibmqj719+CqhL5fIn/tQG7k7YbdhlMFkI8\nFgkIk5ROp5CVY6Oxthu364600dIC0OvpPlFJ+Jy5mBIS/K/d3k9B0kVCiMchAWESy8q14fGoNNR0\n+cv0ERFEzPPthHbno6bgSxfFxUcQFRM2oe0UQjwdJCBMYompkYRHmAImqQHEbNhIUvlGwmbP8ZfZ\nex20t/RL70AI8dgmdMc08WgURSEz18alMy24nB5MIb4fl3l6GrZFcwI2/6i94ksXZUtAEEI8Jukh\nTHLZeTa8Xo36a133rVdb3U58ogVrVOh96wkhxL1IQJjkEpKsRFhDRqWN7tTXM0xH24CsbCqEGBMJ\nCJOcoihk5dpoqu/B6XDftY7/6SIJCEKIMZCAMAVk59lQVY36q3dPG9VUt5OQbMUSaZ7glgkhniYS\nEKYA2zQLlkjzqElqAD1dQ3S1D0rvQAgxZhIQpgBFUcjOs3GjoQfHcGDaSNJFQojxIgFhisjKtaFp\nvr0O7lRT3U5iSiQRlpB7HCmEEA9HAsIUEZcQQWR0aEDaqLtjkJ7OIZl7IIQYFxIQpghFUcjKs9HS\n2MvQoG8bzZrqdhQFMnMkIAghxk4CwhSSfUfaSNM0ai93kJgaRViEKdhNE0I8BSQgTCExtnCiY8Oo\nrW7nZms/vd3Dki4SQoybMQeEv/3bv2XdunVs3LiRV199lQsXLtyz7rvvvktpaSmlpaW8++67Y730\nM+f2JLWWpj4qD9XdShfFBbtZQoinxJgDwsqVK/n000/ZsWMHP/zhD3nrrbfuWq+qqordu3ezc+dO\ndu7cye7du6mqqhrr5Z85t3sE56pukJwWTWiYpIuEEONjzAFh1apVGI1GAPLz82lra0NV1VH1du3a\nRXl5OWazGbPZTHl5Obt27Rrr5Z850XHhxNh822NKukgIMZ7GdfnrDz/8kOeffx6dbnScaW1tZenS\npf7vExMTH6uHEBsbMaY2Pg0WLU/j4J6rLClMlx7CLTabJdhNmDTkXoyQe/FoHhgQNm/eTEtLy11f\nO3bsGHq9HoDPPvuMTz/9lA8//HB8W/gNXV0DqKr2RK8x2WXlxZG/JIWBQScDg85gNyfobDZLwN4Q\nzzK5FyPkXvjodMpD/yP9wIDwySefPPAkX3zxBe+88w7vv/8+cXF3H+RMTEwMCCytra0kJiY+VCNF\nIEVRCA0zSTAQQoyrMY8h7N+/n3/8x3/kvffeIyUl5Z711q1bx7Zt23A4HDgcDrZt28b69evHenkh\nhBDjZMxjCD/96U8xGo385Cc/8Ze9//77REdH87Of/YySkhJWr17NsmXLWLNmDS+99BIA5eXlAWMK\nQgghgkvRNG1KJeRlDMFH8qMj5F6MkHsxQu6Fz6OMIchMZSGEEIAEBCGEELdIQBBCCAGM88S0iaDT\nKcFuwqQh92KE3IsRci9GyL14tHsw5QaVhRBCPBmSMhJCCAFIQBBCCHGLBAQhhBCABAQhhBC3SEAQ\nQggBSEAQQghxiwQEIYQQgAQEIYQQt0hAEEIIAUyhgFBfX88rr7zC2rVreeWVV2hoaAh2k4Li5z//\nOSUlJeTk5HCQYTBiAAADZ0lEQVT16tVgNyeoenp6+P73v8/atWvZsGEDP/rRj+ju7g52s4LmjTfe\nYOPGjZSXl7Nlyxaqq6uD3aSg+uUvfyl/J0BJSQnr1q1j06ZNbNq0icOHD9+7sjZFfOc739G2bdum\naZqmbdu2TfvOd74T5BYFR1VVldbS0qKtWrVKu3LlSrCbE1Q9PT3aiRMn/N//0z/9k/bTn/40iC0K\nLrvd7v/6iy++0MrLy4PYmuC6ePGi9vrrr8vfiaY90j2YEj2Erq4uLl26RFlZGQBlZWVcunTpmfxv\ncPHixbIX9S1RUVEsW7bM/31+fn7Avt3PGovF4v96YGAARXk2F3ZzuVy8/fbb/M3f/E2wmzLlTInV\nTltbW0lISECv1wOg1+uJj4+ntbWVmJiYILdOTAaqqvLRRx9RUlIS7KYE1c9+9jOOHj2Kpmn89re/\nDXZzgmLr1q1s3Ljxvnu8P2v+4i/+Ak3TWLRoEX/+53+O1Wq9a70p0UMQ4kH+7u/+jrCwMF577bVg\nNyWo/uEf/oEDBw7w1ltv8Ytf/CLYzZlwZ86c4eLFi2zZsiXYTZk0PvzwQ3bs2MEf/vAHNE3j7bff\nvmfdKREQEhMTuXnzJl6vFwCv10t7e7ukTgTgG2i/fv06//Iv/4JONyV+pZ+48vJyKisr6enpCXZT\nJlRVVRW1tbWsXr2akpIS2traeP311zly5EiwmxY0tz8nTSYTW7Zs4fTp0/esOyX+emJjY8nLy2Pn\nzp0A7Ny5k7y8PEkXCf75n/+Zixcv8u6772IymYLdnKAZHByktbXV/31FRQWRkZFERUUFsVUT7wc/\n+AFHjhyhoqKCiooKpk2bxnvvvUdxcXGwmxYUQ0ND9Pf3A6BpGrt27SIvL++e9afMBjm1tbX81V/9\nFXa7HavVys9//nMyMzOD3awJ9/d///fs3buXzs5OoqOjiYqK4rPPPgt2s4Li2rVrlJWVkZ6ejtls\nBiAlJYV33303yC2beJ2dnbzxxhsMDw+j0+mIjIzkL//yL5k9e3awmxZUJSUl/PrXv2bmzJnBbkpQ\nNDU18eMf/xiv14uqqmRlZfHXf/3XxMfH37X+lAkIQgghnqwpkTISQgjx5ElAEEIIAUhAEEIIcYsE\nBCGEEIAEBCGEELdIQBBCCAFIQBBCCHGLBAQhhBAA/H+Fht5SWNlFiQAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "0FOe0lYrrOXp",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        ""
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "bFeMPrLMrKze",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        ""
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "_bbB99gS4Gku",
        "colab_type": "text"
      },
      "source": [
        "# Exercises"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "pOLW04W-OYME",
        "colab_type": "text"
      },
      "source": [
        "## 1. Generate a time series from an IID Gaussian random process. This is a memoryless, stationary series:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "eXyrtcKtO4uE",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "import numpy.random as rn"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "tFBm0EVYPNYH",
        "colab_type": "code",
        "outputId": "4cf50f71-38c7-4a6a-dd3d-9bd3ffdd6ff2",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        }
      },
      "source": [
        "df = pd.DataFrame()\n",
        "ret = rn.randn(1000)\n",
        "df['ret'] = ret\n",
        "df.describe()"
      ],
      "execution_count": 6,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>ret</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>count</th>\n",
              "      <td>1000.000000</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>mean</th>\n",
              "      <td>-0.041682</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>std</th>\n",
              "      <td>1.021973</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>min</th>\n",
              "      <td>-3.845281</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>25%</th>\n",
              "      <td>-0.716426</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>50%</th>\n",
              "      <td>-0.022915</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>75%</th>\n",
              "      <td>0.642146</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>max</th>\n",
              "      <td>3.713729</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "               ret\n",
              "count  1000.000000\n",
              "mean     -0.041682\n",
              "std       1.021973\n",
              "min      -3.845281\n",
              "25%      -0.716426\n",
              "50%      -0.022915\n",
              "75%       0.642146\n",
              "max       3.713729"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 6
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "V5abr9JMQ3OV",
        "colab_type": "code",
        "outputId": "903bb3b4-49ce-42c2-a64a-468f2ea08099",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        }
      },
      "source": [
        "df.plot()"
      ],
      "execution_count": 7,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.axes._subplots.AxesSubplot at 0x7f430532d9e8>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 7
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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NYK+paUYkIqEuNlIfamjHVQ98bNikubVNO3nVbREOtrpaq53Ir2bLLvqGBHUN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\nHA4nzeCCncPhcNIMLtg5HA4nzfj/gbaNPCKGyZsAAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ZG-BgJMkObQP",
        "colab_type": "text"
      },
      "source": [
        "### (a) Compute the ADF statistic on this series. What is the p-value?"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ChRw-cD6O3ki",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "from statsmodels.tsa.stattools import adfuller as adf"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "o6PQj9EbRKHi",
        "colab_type": "code",
        "outputId": "eb00adb5-fe58-4720-c44d-e901d9a16d29",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        }
      },
      "source": [
        "stat = adf(df.ret)\n",
        "stat"
      ],
      "execution_count": 9,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(-23.712512183587858,\n",
              " 0.0,\n",
              " 1,\n",
              " 998,\n",
              " {'1%': -3.4369193380671, '10%': -2.56831430323573, '5%': -2.864440383452517},\n",
              " 2817.9533083591687)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 9
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "j7e-rTwmRHgM",
        "colab_type": "code",
        "outputId": "06cbee30-a4c2-4108-99ea-65f8289d4217",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        }
      },
      "source": [
        "print('p-value:', stat[1])"
      ],
      "execution_count": 10,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "p-value: 0.0\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "CJjLIfD2RtSl",
        "colab_type": "text"
      },
      "source": [
        "### (b) Compute the cumulative sum of the observations. This is a non-stationary series without memory."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "seuaETVXR4O3",
        "colab_type": "code",
        "outputId": "c2d618aa-2cec-441e-bf69-a1b8167f2f4b",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        }
      },
      "source": [
        "df['cumsum'] = ret.cumsum()\n",
        "df.plot()"
      ],
      "execution_count": 11,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.axes._subplots.AxesSubplot at 0x7f4303bae630>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 11
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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Q6/LH4eKw61ABhvRKxje/Hkf/rgl49/v9GHdJO3l0furvA9GtnZiv/KvVR+Rj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\noE9EZCAM+kREBsKgT0RkIAz6REQG8v9p+OMZA8T8MAAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ofMcHp50R1bc",
        "colab_type": "text"
      },
      "source": [
        "(i) What is the order of integration of this cumulative series?\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "FhoBiRZqR3Hc",
        "colab_type": "text"
      },
      "source": [
        "(ii) Compute the ADF statistic on this series. What is the p-value?"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "O-_YGlD1SPeu",
        "colab_type": "code",
        "outputId": "57a4efff-655d-4a53-9725-7ab67908f608",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        }
      },
      "source": [
        "print('p-value: ',adf(df['cumsum'])[1])"
      ],
      "execution_count": 12,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "p-value:  0.9635662056545087\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "1DFUf0qiSo-I",
        "colab_type": "code",
        "outputId": "b1ebe4bc-b1da-4be8-9d9c-dd7972027134",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        }
      },
      "source": [
        "#'1d' --> I(1)\n",
        "\n",
        "oned = df['cumsum'].diff().dropna()\n",
        "print('p-value: ', adf(oned)[1])"
      ],
      "execution_count": 13,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "p-value:  0.0\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "okGEVtSIT5fn",
        "colab_type": "text"
      },
      "source": [
        "### (c) Differentiate the series twice. What is the p-value of this over-differentiated series?"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "81yB45qFUghA",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "diff2 = df['ret'].diff().diff().dropna()"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ei6h7ZO3h7Ef",
        "colab_type": "code",
        "outputId": "1d9e5a08-3ea3-4d6d-95d0-615736ceb5fe",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        }
      },
      "source": [
        "diff2.plot()"
      ],
      "execution_count": 15,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.axes._subplots.AxesSubplot at 0x7f43010d1748>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 15
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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BU/yRhB9WGIcW5XBGMBfIopGptcwpuJJuAGTaN7G6tHJLLg6fkvbLbywGHTPL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\nV4R1FQAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "H_daIJuFUqt1",
        "colab_type": "code",
        "outputId": "eca9f964-49ba-466b-a31a-36c88c6e2250",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        }
      },
      "source": [
        "print('p-value: ',adf(diff2)[1])"
      ],
      "execution_count": 16,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "p-value:  1.413109630508856e-27\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "KX5nxDGRVOww",
        "colab_type": "text"
      },
      "source": [
        "## 2. Generate a time series that follows a sinusoidal function. This is a stationary series with memory."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "lZylpNuPU0VJ",
        "colab_type": "code",
        "outputId": "453e9857-ac5c-48a1-d9bb-aa3c7d40baf5",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        }
      },
      "source": [
        "sin = np.sin(np.linspace(1,25,1000))\n",
        "df['sin'] = sin\n",
        "df['sin'].plot()"
      ],
      "execution_count": 17,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.axes._subplots.AxesSubplot at 0x7f43010b9c88>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 17
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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W7Gvf+MY38IMf/AAqlQrHjh3DPffcg0OHDsFszn0/IBiMFhRpYDOymvLHn3uwLse8/GKE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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "usPhNEXmV6VK",
        "colab_type": "code",
        "outputId": "9ada9924-c4c6-4762-ba12-66bd9223682c",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        }
      },
      "source": [
        "df[['sin']].describe()"
      ],
      "execution_count": 18,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>sin</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>count</th>\n",
              "      <td>1000.000000</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>mean</th>\n",
              "      <td>-0.018413</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>std</th>\n",
              "      <td>0.715700</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>min</th>\n",
              "      <td>-0.999999</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>25%</th>\n",
              "      <td>-0.729817</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>50%</th>\n",
              "      <td>-0.062795</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>75%</th>\n",
              "      <td>0.714026</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>max</th>\n",
              "      <td>0.999992</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "               sin\n",
              "count  1000.000000\n",
              "mean     -0.018413\n",
              "std       0.715700\n",
              "min      -0.999999\n",
              "25%      -0.729817\n",
              "50%      -0.062795\n",
              "75%       0.714026\n",
              "max       0.999992"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 18
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "C5xgcsTdW8hH",
        "colab_type": "text"
      },
      "source": [
        "### (a) Compute the ADF statistic on this series. What is the p-value?"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "3pbiuzrZW_R4",
        "colab_type": "code",
        "outputId": "fdf1cacf-b07a-466d-b0d9-6e8a64f0fdcd",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        }
      },
      "source": [
        "print('p-value:', adf(df['sin'])[1])"
      ],
      "execution_count": 19,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "p-value: 0.0\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ErAeBQtTXLNq",
        "colab_type": "text"
      },
      "source": [
        "### (b) Shift every observation by the same positive value. Compute the cumulative sum of the observations. This is a non-stationary series with memory."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "psa9_iKHWlLS",
        "colab_type": "code",
        "outputId": "21526ef1-b7e4-40d5-95af-bd3ce5fd873f",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        }
      },
      "source": [
        "df['sin2'] = (df['sin'] + 1).cumsum()\n",
        "\n",
        "plt.plot(df['sin2']) "
      ],
      "execution_count": 20,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x7f42ffd3da20>]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 20
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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IYcd0Ok6RJxJC4HfvVqO9axCPrJjDK4TI41wKAofDgaamJmRlZeHxxx9HeXk5HnjgAWzZ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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "SHd16af2Z0wo",
        "colab_type": "text"
      },
      "source": [
        "(i) Compute the ADF statistic on this series. What is the p-value?\n",
        "\n",
        "(ii) Apply an expanding window fracdiff, with 𝜏 = 1E − 2. For what minimum\n",
        "d value do you get a p-value below 5%?\n",
        "\n",
        "(iii) Apply FFD, with 𝜏 = 1E − 5. For what minimum d value do you get a\n",
        "p-value below 5%?"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "zDUzmuX1XpeX",
        "colab_type": "code",
        "outputId": "f5a6e24a-1f3c-4442-e9c8-170927aafc8d",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        }
      },
      "source": [
        "# (i)\n",
        "print('p-value:', adf(df['sin2'])[1])"
      ],
      "execution_count": 21,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "p-value: 1.0\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "qNV-7Bn3Z_iT",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "outputId": "762aca1f-626e-4cc3-af61-2c328e9e58ca"
      },
      "source": [
        "#(ii) & (iii)\n",
        "# I will import the function from mlfinlab\n",
        "!pip install -q mlfinlab\n",
        "import mlfinlab\n",
        "fracdiff = mlfinlab.fracdiff"
      ],
      "execution_count": 22,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "\u001b[?25l\r\u001b[K     |██▊                             | 10kB 27.9MB/s eta 0:00:01\r\u001b[K     |█████▌                          | 20kB 1.7MB/s eta 0:00:01\r\u001b[K     |████████▎                       | 30kB 2.4MB/s eta 0:00:01\r\u001b[K     |███████████                     | 40kB 1.6MB/s eta 0:00:01\r\u001b[K     |█████████████▉                  | 51kB 2.0MB/s eta 0:00:01\r\u001b[K     |████████████████▋               | 61kB 2.3MB/s eta 0:00:01\r\u001b[K     |███████████████████▍            | 71kB 2.7MB/s eta 0:00:01\r\u001b[K     |██████████████████████▏         | 81kB 3.1MB/s eta 0:00:01\r\u001b[K     |█████████████████████████       | 92kB 3.4MB/s eta 0:00:01\r\u001b[K     |███████████████████████████▊    | 102kB 2.6MB/s eta 0:00:01\r\u001b[K     |██████████████████████████████▌ | 112kB 2.6MB/s eta 0:00:01\r\u001b[K     |████████████████████████████████| 122kB 2.6MB/s \n",
            "\u001b[?25h"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "orLA2S4ZbrKn",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# (ii)\n",
        "t1 = 1e-2"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "FprksQ8rgiVn",
        "colab_type": "code",
        "outputId": "fcd1f71e-1dbf-4b9f-ffb2-d087c0e556b4",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        }
      },
      "source": [
        "for d in np.arange(0, 1.0, 0.05):\n",
        "    s = fracdiff.frac_diff(df[['sin2']], d, thresh=t1).dropna()\n",
        "    p_val = adf(s['sin2'])[1]    \n",
        "    if p_val < 0.05:\n",
        "        print(\"The minimum d value with a p-value below 5% is:\")\n",
        "        print(d)\n",
        "        break"
      ],
      "execution_count": 24,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "The minimum d value with a p-value below 5% is:\n",
            "0.1\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "1DscN54fg1sR",
        "colab_type": "code",
        "outputId": "d49f0bd4-0317-4e7d-a0d8-641a67950ea0",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        }
      },
      "source": [
        "f1 = fracdiff.frac_diff(df[['sin2']], 0.1, thresh=t1).dropna()\n",
        "f1.plot()"
      ],
      "execution_count": 25,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.axes._subplots.AxesSubplot at 0x7f42f912ad30>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 25
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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djhDCRUjYe5Cm1g42v3+YmHB/bp8hNyMRQvyLhL2HUFWVP+8qpKG5nfszxuPr\nLdMshRD/ImHvIfYesvD1kWrmX5UoNyMRQvwHCXsPUFnXwusfHmXsiFBmXTrC2eUIIVyQhL2b67Qr\nvPxeAV4GHYvnjEMv0yyFEOcgYe/m3vu8lJLyBu5OH0t48DBnlyOEcFH9CvvMzEySkpIoKiri+PHj\nLFy4kPT0dObMmcPKlSux2Wzd22ZlZZGens7111/P0qVLaW1tdXjxWld0qp7t/yzligkxXDI2ytnl\nCCFcWJ/DPj8/n9zcXMxmMwDe3t6sXLmSXbt2sW3bNlpbW9m8eTMAzc3NPPHEE2zatIkPP/yQgICA\n7nXCMZpaO3hxWz7GUD/uvG6Ms8sRQri4PoV9e3s769atY+3atd3L4uLiGDduXNeT6PWkpqZSXl4O\nwKeffkpKSgoJCQkALFiwgJ07dzq2cg1TVZU/7jhMQ3M7P547Hj9fL2eXJIRwcX1KiY0bN5KRkUFc\n3LkvqGWz2di6dSuPPfYYABaLhdjY2O71sbGxWCyWfhcXETH0V2o0Gl1/2uL2vSXsP1rD4rkpXDLB\nPODnc4eeB4MW+5aeteu8Yb9//37y8vJYtmzZOdd3dnby05/+lMsuu4yZM2c6tDirtQlFUR36nL0x\nGoOorm4cste7ECcrG9m8LY+JoyK4fKxxwPW6Q8+DQYt9S8+eT6/X9XiQfN5hnOzsbIqLi5k5cyYz\nZsygoqKCRYsWsXfvXux2O8uWLSMkJISf//zn3Y8xmUzdQzoA5eXlmEwmB7Sibbb2Tja9m0+gnzf3\nzZarWQoh+u68Yb9kyRL27t1LVlYWWVlZxMTEsHnzZqZNm8aKFSswGAw8+eSTZwXP9OnTOXToEKWl\npQBs2bKFG2+8cdCa0IrXPiyisraFJTePJ8jfx9nlCCHcyAV/s/fpp5+ybds2xowZw/z58wGYPHky\na9asITAwkHXr1nH//fejKArJycmsWrXKYUVr0T/zKvj8UAUZVyQwNj7M2eUIIdyMTlXVoRsU7ycZ\ns+9SWdvC2j9lEx8VyPI7L8agd9y5cK7a82DTYt/Ss+cb0Ji9cK6OToVN7+bjpdexJGO8Q4NeCKEd\nkhwu7m8fH+NEZSP33ZQsl0MQQlwwCXsXllNYxUc5ZVw3JY6LxxidXY4Qwo1J2LuoytoW/rDjMImx\nwdwmd50SQgyQhL0Lau+w89zbeRj0Oh6Ym4KXQXaTEGJgJEVc0GsfFlFW3cSPbh5PRIiM0wshBk7C\n3sV8fsjCZwctzJkWT+qoCGeXI4TwEBL2LqSsqom/7D7C2BGh3HJlorPLEUJ4EAl7F9Ha1slz7+Th\n5+vF/Rnj0evlujdCCMeRsFYIy+cAAA4ASURBVHcBqqryx52FVNW18OO54wkJ9HV2SUIIDyNh7wJ2\nfXWSnMIqfnD1KJJGyHVvhBCOJ2HvZPnHa3nr42LSxkaRfukIZ5cjhPBQEvZOVF3fyqZ384iNDOC+\nm8bK9emFEINGwt5J2jrsZP79EKoKD8+fwDAfuY+sEGLwSNg7gaqq/HlnIWVVTSzJGE90mL+zSxJC\neDgJeyf4MPsU+woqmXdVopw4JYQYEhL2Q+xwaS1v7ilmyhgjsy+Pd3Y5QgiNkLAfQlV1Lbzwbj7R\n4X5yw3AhxJCSsB8iLbZONr51EFVVeeTWVPx85QtZIcTQkbAfAnZFYdO7eVTVtfLgvAlEh8sXskKI\noSVhPwTe+Mcx8o7XctcNY0iOlzNkhRBDr19hn5mZSVJSEkVFRQDk5uaSkZHBrFmzuO+++7Bard3b\n9rZOS/bsP81HX5dxfdpwrp5kdnY5QgiN6nPY5+fnk5ubi9ncFViKorB8+XJWr17N7t27SUtL49ln\nnz3vOi05XFrLax8UkToqgtvl1oJCCCfqU9i3t7ezbt061q5d270sLy8PX19f0tLSAFiwYAG7du06\n7zqtOF3dRObbecRE+Msli4UQTtensN+4cSMZGRnExcV1L7NYLMTGxnb/HB4ejqIo1NfX97pOC+oa\n2/jN3w7g46Vn6Q9l5o0QwvnOm0L79+8nLy+PZcuWDUU9Z4mICBzy1zQagwb0+BZbB798JYfWtk6e\nfvBKRsWFOqiywTPQnt2VFvuWnrXrvGGfnZ1NcXExM2fOBKCiooJFixaxcOFCysvLu7erra1Fr9cT\nGhqKyWTqcV1/WK1NKIrar8cMhNEYRHV14wU/vtOusPFvBzhhaWTpD1MJ9jUM6PmGwkB7dlda7Ft6\n9nx6va7Hg+TzDuMsWbKEvXv3kpWVRVZWFjExMWzevJnFixdjs9nIyckBYMuWLaSnpwOQkpLS4zpP\n9d3FzfJL67jnxiRSEuWaN0II13HBg8l6vZ7169ezZs0a2traMJvNbNiw4bzrPNXbn5XweV4Fc68c\nyfTU2PM/QAghhpBOVdWhGyfpJ3cZxtn91UneyDrGVRNN3JPuXjch0drH3O9osW/p2fMNaBhH9O6z\nA+W8kXWMtCQjd89yr6AXQmiHhP0A5BRW8addhYwfGc6Pbpa59EII1yVhf4HySqy8uC2fUbEhPDxv\nAt5e8l8phHBdklAX4GhZPZlvHyI2MoClP0zF18fg7JKEEKJXEvb9dKzsDL958wBhgb48dvsk/Id5\nO7skIYQ4Lwn7fjhWdoZfv5lLcIAPP7tzMiEBPs4uSQgh+kTCvo+Onf5X0P/3nZMJC/J1dklCCNFn\nEvZ9cOz0GX79hgS9EMJ9yeUYz+Pfh24k6IUQ7krCvhd5JVYy3z5EWKAvP5OgF0K4MQn7Hnx1uJKX\n3yvAHBnAT2+fJF/GCiHcmoT9OXyce5q/7DrC6LgQHv1BqkyvFEK4PQn779mx7wRvfVzMhMQIHpyX\ngq+3nDAlhHB/EvbfUhSVl945xHuflXDpuGgWzU7GyyCTlYQQnkHCHmht6+TFbfkcLLZyfdpwbp85\nGr1cvVII4UE0H/a1DTY2vnWQ09XNPHBrKpdcFOnskoQQwuE0HfYnKhr57VsHaGu38+gPU5lxaYKm\nbnQghNAOzYZ9dmEVm98vIMjPm8fvmkJc1Lnv7iKEEJ5Ac2FvVxTe+riY3V+dYpQ5mIfnTSAkUE6W\nEkJ4Nk2F/Znmdl58N4/Ck/XMmGxmwcyLZMaNEEITNBP2h0/U8fJ7+bTYOlk8J5lpKSZnlySEEEOm\nT2H/4IMPUlZWhl6vx9/fnyeeeILk5GT27NnDxo0bUVUVVVV5+OGHueGGGwA4fvw4K1asoL6+ntDQ\nUJ555hkSEhIGs5dz6rQrvLv3ODv+eYLocH+W/nAiI6KDhrwOIYRwJp2qqur5NmpsbCQoqCsgP/ro\nI5577jn+/ve/M3XqVF577TXGjBlDYWEhd9xxB19//TV6vZ67776bW2+9lblz5/Luu++ydetWXnnl\nlX4VZ7U2oSjnLa9HVfWtvLwtn+LyBqanmrjzujG93kLQaAzS3GwcLfYM2uxbevZ8er2OiIhzTzbp\n04D1d0EP0NTUhO7bE470ej2NjV3/kY2NjURFRaHX67FarRQUFDBnzhwA5syZQ0FBAbW1tQNqpK8U\nVSXrmzLWbP6KcmsLP547nv9zU7LcK1YIoVl9HrNftWoVn3/+Oaqq8vvf/x6dTsdvf/tbHnzwQfz9\n/Wlubuall14CwGKxEB0djcHQFa4Gg4GoqCgsFgvh4eGD08m3qupb+dOOwxSerCdlZDj3pI8lImTY\noL6mEEK4uj6H/ZNPPgnAO++8w/r163nhhRd48cUXef7555kyZQpff/01S5cu5f3333dYcT19HDmX\nTrvCtk9LeP2DQgx6HY/cNonrpo7o/hTSV0aj9sbztdgzaLNv6Vm7+j0b55ZbbmH16tXk5+dTVVXF\nlClTAJgyZQp+fn4UFxdjNpuprKzEbrdjMBiw2+1UVVVhMvVvBkxfx+wLT9Tx6odFlNc0M2l0JHfd\nMIbw4GHU1DT16/W0Nr4H2uwZtNm39Oz5BjRm39zcjMVi6f45KyuLkJAQTCYTFRUVlJSUAFBcXIzV\namXEiBFERESQnJzM9u3bAdi+fTvJyckOH8KpqW/lxW35rP/rfto77Dzyg1Qe+UEq4cEybCOEEP/u\nvEf2ra2tPProo7S2tqLX6wkJCWHTpk1ERUWxdu1aHn300e6hkqeeeorQ0FAA1q5dy4oVK3j++ecJ\nDg7mmWeecVjRTa0dbP+ilKxvytDpdNw8LYHZl8fjI9eeF0KIc+rT1Etn+f4wToutk398U8auL09i\na+/kihQTt0wf6bAjea195ANt9gza7Ft69ny9DeO4xRm0jS3tfJhTxj++LqO1rZOJoyK49ZpRxBnl\n4mVCCNEXLh32lXWt7PryBF8cqqC9w87kJCNzLk8gPka+XRdCiP5w6bD/3y37qW1o49LkKNIvi8cc\nGeDskoQQwi25dNjfeOkILh5jJNjfx9mlCCGEW3PpsL92ctyAro0jhBCii1zMXQghNEDCXgghNEDC\nXgghNEDCXgghNEDCXgghNEDCXgghNEDCXgghNMCl59nr9f278Yi7vqazabFn0Gbf0rNn661Xl77q\npRBCCMeQYRwhhNAACXshhNAACXshhNAACXshhNAACXshhNAACXshhNAACXshhNAACXshhNAACXsh\nhNAAl75cgiOVlZXx0EMPdf/c2NhIU1MTX331FTNmzMDHxwdfX18Ali1bxvTp0wHIzc1l9erVtLW1\nYTab2bBhAxEREU7p4ULs2bOHjRs3oqoqqqry8MMPc8MNN3D8+HFWrFhBfX09oaGhPPPMMyQkJAD0\nus4d9NSzJ+/njz/+mI0bN9LZ2UlISAhPP/00w4cP9+j9DD337cn7+oKpGvWrX/1K/cUvfqGqqqpe\ne+216pEjR/5jG7vdrl533XVqdna2qqqq+txzz6krVqwY0joHQlEUNS0trbu3w4cPq5MmTVLtdru6\ncOFC9Z133lFVVVXfeecddeHChd2P622dq+utZ0/dz/X19erUqVPVkpISVVW79tl9992nqmrv+9Kd\n97Oq9t63p+7rgdDkME57ezvvvfcet956a6/b5eXl4evrS1paGgALFixg165dQ1Giw+j1ehobG4Gu\nTzNRUVHU1dVRUFDAnDlzAJgzZw4FBQXU1tZitVp7XOcuztWzXt/zW93d9/OJEyeIjIxk5MiRAFx9\n9dXs3bu3133pCfu5p75768Hd9/VAaGYY599lZWURHR3N+PHju5ctW7YMVVWZMmUKjz32GMHBwVgs\nFmJjY7u3CQ8PR1GU7o+9rk6n0/Hb3/6WBx98EH9/f5qbm3nppZewWCxER0djMBgAMBgMREVFYbFY\nUFW1x3Xh4eHObKdPeur5O564n0eOHElNTQ0HDx4kNTWV9957D8Cj9zP03jd45r4eCE0e2W/duvWs\no/rXXnuNbdu2sXXrVlRVZd26dU6sznE6Ozt58cUXef7559mzZw8vvPACS5cupaWlxdmlDZqeem5u\nbvbY/RwUFMRvfvMbnn76aebPn4/VaiU4ONij9zP03LfBYPDYfT0Qmjuyr6ysJDs7m/Xr13cvM5lM\nAPj4+HDnnXfywAMPdC8vLy/v3q62tha9Xu82RwCHDx+mqqqKKVOmADBlyhT8/Pzw9fWlsrISu92O\nwWDAbrdTVVWFyWRCVdUe17mDnnouLi4mNTUV8Lz9DDBt2jSmTZsGQE1NDZs3b8ZsNnvsfv7Oufoe\nMWIE/v7+gGfu6wuluSP7t99+m6uvvpqwsDAAWlpausd3VVVlx44dJCcnA5CSkoLNZiMnJweALVu2\nkJ6e7pzCL0BMTAwVFRWUlJQAUFxcjNVqJT4+nuTkZLZv3w7A9u3bSU5OJjw8nIiIiB7XuYOeeo6O\njvbY/QxQXV0NgKIo/PrXv2bBggWYzWaP3c/fOVffgEfv6wuluZuXzJo1i1WrVnHVVVcBcOrUKX7y\nk59gt9tRFIVRo0bx85//nKioKAC++eYb1qxZc9Y0rcjISGe20C/btm3j5ZdfRqfruoPNI488wnXX\nXUdxcTErVqygoaGB4OBgnnnmGRITEwF6XecOztVzUlKSR+/nVatW8c0339DR0cEVV1zB//zP/+Dr\n6+vR+xnO3XdVVZVH7+sLpbmwF0IILdLcMI4QQmiRhL0QQmiAhL0QQmiAhL0QQmiAhL0QQmiAhL0Q\nQmiAhL0QQmiAhL0QQmjA/wdBb9v40ujDJQAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "d5Qzlnlwkw41",
        "colab_type": "code",
        "outputId": "d41cb4bc-545e-4fca-8e27-c167267987b7",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        }
      },
      "source": [
        "f1"
      ],
      "execution_count": 26,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>sin2</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>726</th>\n",
              "      <td>374.243743</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>727</th>\n",
              "      <td>374.570715</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>728</th>\n",
              "      <td>374.913784</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>729</th>\n",
              "      <td>375.273030</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>730</th>\n",
              "      <td>375.648524</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>...</th>\n",
              "      <td>...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>995</th>\n",
              "      <td>501.273976</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>996</th>\n",
              "      <td>501.708453</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>997</th>\n",
              "      <td>502.159418</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>998</th>\n",
              "      <td>502.626882</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>999</th>\n",
              "      <td>503.110846</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "<p>274 rows × 1 columns</p>\n",
              "</div>"
            ],
            "text/plain": [
              "           sin2\n",
              "726  374.243743\n",
              "727  374.570715\n",
              "728  374.913784\n",
              "729  375.273030\n",
              "730  375.648524\n",
              "..          ...\n",
              "995  501.273976\n",
              "996  501.708453\n",
              "997  502.159418\n",
              "998  502.626882\n",
              "999  503.110846\n",
              "\n",
              "[274 rows x 1 columns]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 26
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Rj16nd08koBC",
        "colab_type": "code",
        "outputId": "6e78ae0e-7827-4b64-cfe5-e489f3219708",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        }
      },
      "source": [
        "adf(f1['sin2'])[1]"
      ],
      "execution_count": 27,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.00022971652953082789"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 27
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "-AzyDXCgfxiU",
        "colab_type": "code",
        "outputId": "3c8ddab9-3e78-41b0-ab74-6044be05c6b1",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        }
      },
      "source": [
        "## (iii)\n",
        "\n",
        "t2 = 1e-5\n",
        "\n",
        "for d in np.arange(0, 2.0, 0.05):\n",
        "    s = fracdiff.frac_diff_ffd(df[['sin2']], d, t2).dropna()\n",
        "    if len(s['sin2']) >= 2:\n",
        "      p_val = adf(s['sin2'])[1]    \n",
        "      if p_val < 0.05:\n",
        "          print(\"The minimum d value with a p-value below 5% is:\")\n",
        "          print(d)\n",
        "          break"
      ],
      "execution_count": 28,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "The minimum d value with a p-value below 5% is:\n",
            "1.0\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "WG4KMwl6hBoV",
        "colab_type": "code",
        "outputId": "c79a8a49-6525-47ea-8f5e-3e79ad9a5481",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        }
      },
      "source": [
        "f2 = fracdiff.frac_diff_ffd(df[['sin2']], 1.0, thresh=t2).dropna()\n",
        "f2.plot()"
      ],
      "execution_count": 29,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.axes._subplots.AxesSubplot at 0x7f42f8f9ad68>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 29
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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g9l6Kn790esHjkvgvACOqXI34mbRM+SlOU1NncxG+hnky0Nk9udm3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\nSUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Qy_lKsdcj-jf",
        "colab_type": "text"
      },
      "source": [
        "### 주가를 사용해 FracDiff를 plot해보자"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ehIX10IxlvwS",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "import datetime as dt\n",
        "import pandas_datareader.data as web"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "iu0XmMQluvrK",
        "colab_type": "code",
        "outputId": "456de156-c458-4134-adc4-36b3f150f17d",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        }
      },
      "source": [
        "start = dt.datetime(2014,1,1)\n",
        "end = dt.datetime(2019,12,1)\n",
        "\n",
        "stock = 'AMZN'\n",
        "\n",
        "df1 = web.DataReader(stock,'yahoo',start,end)\n",
        "df1 = df1[['Adj Close']]\n",
        "\n",
        "ld = df1.pct_change().dropna()\n",
        "\n",
        "fig, ax1 = plt.subplots( figsize=(10,6))\n",
        "ax1.plot(df1, label=stock)\n",
        "ax2 = ax1.twinx()\n",
        "ax2.plot(ld, label=\"log diff\",c='purple',alpha=0.6)\n",
        "fig.legend(loc=\"upper left\")\n",
        "plt.show()"
      ],
      "execution_count": 31,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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BMh+NWSOEZBg+pSE44O1v7m6sx/d1k4ufyEHOG2HBg9YAYJApvhq3wYLzcBNN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\nYII=\n",
            "text/plain": [
              "<Figure size 720x432 with 2 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "-_pSlodZvKC-",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "fr1 = fracdiff.frac_diff(df1,0.7, 1).dropna()\n",
        "fr2 = fracdiff.frac_diff(df1, 0.7, 1e-2).dropna()\n",
        "fr3 = fracdiff.frac_diff_ffd(df1, 0.7, 1e-5).dropna()"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "TrPDf3YQ0Oos",
        "colab_type": "code",
        "outputId": "6980fb0a-bf63-4aa3-b83b-5b0855aa5e14",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        }
      },
      "source": [
        "fig, ax1 = plt.subplots( figsize=(10,6))\n",
        "ax1.plot(df1, label=stock)\n",
        "ax2 = ax1.twinx()\n",
        "ax2.plot(fr1, label=\"Fracitional difference without expanding window\",c='r',alpha=0.6)\n",
        "fig.legend(loc=\"upper left\")\n",
        "plt.show()"
      ],
      "execution_count": 33,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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RICIiCmCllSaEBKmaPC48RF1zvP/lmhpM9qBcrZIjJEgp3ktjSitNAGqrSdyS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\nrmnKQ0ryAAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 720x432 with 2 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "UQGw8l3mvb91",
        "colab_type": "code",
        "outputId": "02122c93-9ea8-4e36-f173-a83c4f140e0f",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        }
      },
      "source": [
        "fig, ax1 = plt.subplots( figsize=(10,6))\n",
        "\n",
        "\n",
        "ax1.plot(df1, label=stock)\n",
        "ax2 = ax1.twinx()\n",
        "ax2.plot(fr2, label=\"Fracitional difference with expanding window (τ=1E-2)\",c='y',alpha=0.8)\n",
        "\n",
        "fig.legend(loc=\"upper left\")\n",
        "\n",
        "\n",
        "plt.show()"
      ],
      "execution_count": 34,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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pMui0Ksy58wqoGAaGFGHEAFuQn/Z5vuPO5qWUW7U7Wcx/ZzcWvLM76PPys1Nk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\n5f8HEYRvkgXjm9QAAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 720x432 with 2 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "qxdFh-gfvf2P",
        "colab_type": "code",
        "outputId": "a1a9ff81-de9b-4c73-a1e8-2687b4eaebd3",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        }
      },
      "source": [
        "fig, ax1 = plt.subplots( figsize=(10,6))\n",
        "\n",
        "\n",
        "ax1.plot(df1, label=stock)\n",
        "ax2 = ax1.twinx()\n",
        "ax2.plot(fr3, label=\"Fraction differnece with fixed window(τ=1E−5)\",c='g', alpha=0.6)\n",
        "\n",
        "fig.legend(loc=\"upper left\")\n",
        "\n",
        "\n",
        "plt.show()"
      ],
      "execution_count": 35,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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i8+ZN0rr29raQ+/gzGAw499yR+Mc/3sHkyZMxduw47Nu3FydOHMPYseepjqejoyPq6wjH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\n",
            "text/plain": [
              "<Figure size 720x432 with 2 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ZRPqHS1f6bsI",
        "colab_type": "code",
        "outputId": "43cbd74c-1773-4213-cb89-d9f2c3c88287",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        }
      },
      "source": [
        "p1= adf(fr1['Adj Close'])[1]\n",
        "p2= adf(fr2['Adj Close'])[1]\n",
        "p3= adf(fr3['Adj Close'])[1]\n",
        "print('p-values of each:',p1,',',p2,',',p3)"
      ],
      "execution_count": 36,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "p-values of each: 9.400866661148138e-07 , 3.7175904795308835e-06 , 5.802863840382561e-06\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "0LC74rWE18OP",
        "colab_type": "text"
      },
      "source": [
        "## 3. Take the series from exercise 2.b:"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "wjhjZ-p42RNT",
        "colab_type": "text"
      },
      "source": [
        "### (a) Fit the series to a sine function. What is the R-squared?\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "SyC8-jmp2U0q",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "from scipy.optimize import curve_fit\n",
        "\n",
        "def fitsin(tt,yy):\n",
        "    ''' Fit sin to the input time sequence, and return fitting parameters \n",
        "    \"amp\", \"omega\", \"phase\", \"offset\", \"freq\", \"period\" and \"fitfunc\"\n",
        "    '''\n",
        "    tt = np.array(tt)\n",
        "    yy = np.array(yy)\n",
        "    ff = np.fft.fftfreq(len(tt), (tt[1]-tt[0]))   # assume uniform spacing\n",
        "    Fyy = abs(np.fft.fft(yy))\n",
        "    guess_freq = abs(ff[np.argmax(Fyy[1:])+1])   # excluding the zero frequency \"peak\", which is related to offset\n",
        "    guess_amp = np.std(yy) * 2.**0.5\n",
        "    guess_offset = np.mean(yy)\n",
        "    guess = np.array([guess_amp, 2.*np.pi*guess_freq, 0., guess_offset])\n",
        "\n",
        "    def sinfunc(t, A, w, p, c):  return A * np.sin(w*t + p) + c\n",
        "    \n",
        "    popt, pcov = curve_fit(sinfunc, tt, yy, p0=guess)\n",
        "    A, w, p, c = popt\n",
        "    f = w/(2.*np.pi)\n",
        "    fitfunc = lambda t: A * np.sin(w*t + p) + c\n",
        "    \n",
        "    return {\"amp\": A, \"omega\": w, \"phase\": p, \"offset\": c, \"freq\": f, \"period\": 1./f, \n",
        "            \"fitfunc\": fitfunc, \"maxcov\": np.max(pcov), \"rawres\": (guess,popt,pcov)}"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "kOaz57H-6rRq",
        "colab_type": "text"
      },
      "source": [
        "https://stackoverflow.com/questions/16716302/how-do-i-fit-a-sine-curve-to-my-data-with-pylab-and-numpy/42322656"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "TvI8wTb_5eqN",
        "colab_type": "code",
        "outputId": "136e38c1-9c00-4949-d89b-8e99d1613e5d",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        }
      },
      "source": [
        "res=fitsin(df.index,df['sin2'])\n",
        "print(res['fitfunc'](df.index))"
      ],
      "execution_count": 38,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Float64Index([ 44.77298450294404,  45.61212005674622,  46.45191784195492,\n",
            "               47.29237679604262,  48.13349585564424,  48.97527395656107,\n",
            "               49.81771003375911,  50.66080302137232,  51.50455185270414,\n",
            "               52.34895546022756,\n",
            "              ...\n",
            "              1006.7119242701417, 1007.6110618746922, 1008.5096445715656,\n",
            "               1009.407671223858,  1010.305140695369, 1011.2020518506034,\n",
            "              1012.0984035547726, 1012.9941946737961, 1013.8894240743016,\n",
            "              1014.7840906236283],\n",
            "             dtype='float64', length=1000)\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "WCAi5DP47KYG",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "df['fitsin'] = res['fitfunc'](df.index)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "sVfCuts-76eu",
        "colab_type": "code",
        "outputId": "a53a3126-2c1a-44be-d6d8-a3da6e641c56",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        }
      },
      "source": [
        "df['sin2'].plot()\n",
        "df['fitsin'].plot()"
      ],
      "execution_count": 40,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.axes._subplots.AxesSubplot at 0x7f42f91eec50>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 40
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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CQAjRbVRLI45963Ed+wJdUBjWGY9iHDoFna7jmeyVdXZefvcw56qbeOTW4Uwf26ebKg4M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\nh3cBlIPrGHUAAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "CLgdhs5P-eCB",
        "colab_type": "code",
        "outputId": "b6800cbd-914e-4d1f-dc78-c9067535ac6d",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        }
      },
      "source": [
        "from sklearn.metrics import r2_score\n",
        "\n",
        "r2 = r2_score(df['sin2'], df['fitsin'])\n",
        "print(\"R2 score:\", r2)"
      ],
      "execution_count": 41,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "R2 score: 0.9901339262608057\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Z6JNob1u_B6Y",
        "colab_type": "text"
      },
      "source": [
        "### (b) Apply FFD(d=1). Fit the series to a sine function. What is the R-squared?"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "jSgx3vc9-xXs",
        "colab_type": "code",
        "outputId": "9062f09e-9bf1-444f-c38d-82152ccd3a57",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        }
      },
      "source": [
        "ffd1 = fracdiff.frac_diff_ffd(df[['sin2']], 1).dropna()\n",
        "fitsin2 = fitsin(ffd1.index, ffd1['sin2'])\n",
        "fitsin2 = fitsin2['fitfunc'](ffd1.index)\n",
        "\n",
        "df3=pd.DataFrame()\n",
        "df3['ffd1'] = ffd1['sin2']\n",
        "df3['fitsin2'] = fitsin2\n",
        "df3.plot()"
      ],
      "execution_count": 42,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.axes._subplots.AxesSubplot at 0x7f42f913ca58>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 42
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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clo5TQeX/i6dBSp8ySa0bY7b1wpbadJCY4ESjbUzIEsDt76MkCxSjrSkIaXvn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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "PP0OedOv_jP7",
        "colab_type": "code",
        "outputId": "b126e6da-b769-4039-9bfa-4e6d7c317372",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        }
      },
      "source": [
        "r2_2 = r2_score(df3['ffd1'], df3['fitsin2'])\n",
        "print(\"R2 score:\", r2_2)"
      ],
      "execution_count": 43,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "R2 score: 1.0\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "4NDeTK9oBAn1",
        "colab_type": "text"
      },
      "source": [
        "### (c) What value of d maximizes the R-squared of a sinusoidal fit on FFD(d). Why?"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "pUAoQjk9Argh",
        "colab_type": "code",
        "outputId": "f820da01-c735-4207-bed7-f49700ca37f0",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        }
      },
      "source": [
        "for d in np.arange(0, 1.001, 0.05):\n",
        "    s = fracdiff.frac_diff_ffd(df[['sin2']], np.round(d,2), thresh=t1).dropna()\n",
        "    fitsin2 = fitsin(s.index, s['sin2'])\n",
        "    fitsin2 = fitsin2['fitfunc'](s.index)\n",
        "    \n",
        "    df3=pd.DataFrame()\n",
        "    df3['ffd1'] = s['sin2']\n",
        "    df3['fitsin2'] = fitsin2\n",
        "    \n",
        "    r2 = r2_score(df3['ffd1'], df3['fitsin2'])   \n",
        "    \n",
        "    print(\"when d is \",np.round(d,2),',', '\\n',\"R2 = \",r2,'\\n')"
      ],
      "execution_count": 44,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "when d is  0.0 , \n",
            " R2 =  0.9901339262608057 \n",
            "\n",
            "when d is  0.05 , \n",
            " R2 =  0.9900890406127287 \n",
            "\n",
            "when d is  0.1 , \n",
            " R2 =  0.9900371672783103 \n",
            "\n",
            "when d is  0.15 , \n",
            " R2 =  0.9899754588728878 \n",
            "\n",
            "when d is  0.2 , \n",
            " R2 =  0.9899113832835658 \n",
            "\n",
            "when d is  0.25 , \n",
            " R2 =  0.9898159751439248 \n",
            "\n",
            "when d is  0.3 , \n",
            " R2 =  0.9897382937913256 \n",
            "\n",
            "when d is  0.35 , \n",
            " R2 =  0.9896351098392058 \n",
            "\n",
            "when d is  0.4 , \n",
            " R2 =  0.9895982670046491 \n",
            "\n",
            "when d is  0.45 , \n",
            " R2 =  0.9894406768044187 \n",
            "\n",
            "when d is  0.5 , \n",
            " R2 =  0.9893851081755205 \n",
            "\n",
            "when d is  0.55 , \n",
            " R2 =  0.9893305503653107 \n",
            "\n",
            "when d is  0.6 , \n",
            " R2 =  0.9890286809848403 \n",
            "\n",
            "when d is  0.65 , \n",
            " R2 =  0.9889214437526223 \n",
            "\n",
            "when d is  0.7 , \n",
            " R2 =  0.9888051501917182 \n",
            "\n",
            "when d is  0.75 , \n",
            " R2 =  0.9880512012493594 \n",
            "\n",
            "when d is  0.8 , \n",
            " R2 =  0.9876597569754004 \n",
            "\n",
            "when d is  0.85 , \n",
            " R2 =  0.9870529037622059 \n",
            "\n",
            "when d is  0.9 , \n",
            " R2 =  0.9858665387298919 \n",
            "\n",
            "when d is  0.95 , \n",
            " R2 =  0.9818298175151948 \n",
            "\n",
            "when d is  1.0 , \n",
            " R2 =  1.0 \n",
            "\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "qD4Lii0xMeLg",
        "colab_type": "text"
      },
      "source": [
        "The r-squared is 1.00 (that is the maximum value). fracDiff_FFD with d=1 makes the series stationary (there is no trend and it is homoscadestic) and since there is no noise the curve fit is complete. \n",
        "\n",
        "https://github.com/jo-cho/advances-in-financial-ml-notes/blob/master/Chapter%2005%20-%20Fractionally%20Differentiated%20Features.ipynb"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "aJnJt-xJO0Kq",
        "colab_type": "text"
      },
      "source": [
        "## 4. Take the dollar bar series on E-mini S&P 500 futures. Using the code in Snippet 5.3, for some d ∈ [0, 2], compute fracDiff_FFD(fracDiff_FFD(series,d),-d). What do you get? Why?"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "lH_ZEIUXPkdg",
        "colab_type": "code",
        "outputId": "b8567fb0-10ab-48d7-d26c-00dee80cd471",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 122
        }
      },
      "source": [
        "from google.colab import drive\n",
        "drive.mount('/content/drive')"
      ],
      "execution_count": 45,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Go to this URL in a browser: https://accounts.google.com/o/oauth2/auth?client_id=947318989803-6bn6qk8qdgf4n4g3pfee6491hc0brc4i.apps.googleusercontent.com&redirect_uri=urn%3aietf%3awg%3aoauth%3a2.0%3aoob&response_type=code&scope=email%20https%3a%2f%2fwww.googleapis.com%2fauth%2fdocs.test%20https%3a%2f%2fwww.googleapis.com%2fauth%2fdrive%20https%3a%2f%2fwww.googleapis.com%2fauth%2fdrive.photos.readonly%20https%3a%2f%2fwww.googleapis.com%2fauth%2fpeopleapi.readonly\n",
            "\n",
            "Enter your authorization code:\n",
            "··········\n",
            "Mounted at /content/drive\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "XQTyp36fO7LV",
        "colab_type": "code",
        "outputId": "cb05bdc4-a24f-4946-c015-7f879a67afb6",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 85
        }
      },
      "source": [
        "from mlfinlab import data_structures, features, filters, labeling\n",
        "\n",
        "#달러 바 만들기 (close)\n",
        "raw_dollar_bars = data_structures.get_dollar_bars('/content/drive/My Drive/Colab Notebooks/csv/clean_IVE_tickbidask2.csv', threshold=1000000)\n",
        "dollar_bars = raw_dollar_bars.set_index(pd.to_datetime(raw_dollar_bars.date_time))\n",
        "dollar_bars = dollar_bars.drop(columns='date_time')\n",
        "dollar_bars = dollar_bars.reset_index().drop_duplicates(subset='date_time', keep='last').set_index('date_time')\n"
      ],
      "execution_count": 46,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Reading data in batches:\n",
            "Batch number: 0\n",
            "Returning bars \n",
            "\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "55S6k8YkQ2Av",
        "colab_type": "code",
        "outputId": "21b230f9-9b44-4d02-b3e3-063c9193e936",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 238
        }
      },
      "source": [
        "rawclose = dollar_bars.close\n",
        "rawclose"
      ],
      "execution_count": 110,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "date_time\n",
              "2009-09-28 09:46:35     51.07\n",
              "2009-09-28 09:53:49     51.14\n",
              "2009-09-28 09:55:26     51.14\n",
              "2009-09-28 10:02:52     51.25\n",
              "2009-09-28 10:10:21     51.29\n",
              "                        ...  \n",
              "2019-06-28 15:58:59    116.56\n",
              "2019-06-28 15:59:02    116.57\n",
              "2019-06-28 15:59:45    116.56\n",
              "2019-06-28 16:00:00    116.57\n",
              "2019-06-28 17:29:22    116.57\n",
              "Name: close, Length: 58607, dtype: float64"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 110
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "weD7WALLP2ra",
        "colab_type": "code",
        "outputId": "bf0d595b-0b00-4e56-dca1-3af49d359586",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 293
        }
      },
      "source": [
        "rawclose.plot()"
      ],
      "execution_count": 111,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.axes._subplots.AxesSubplot at 0x7f42ed532eb8>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 111
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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eVQabslcHtIVAwEdEB5/6NyYWj5I9MShRtVgh0U99qSPCQ3yQlV+GGw/y8ByN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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "6vJCpo5NP8_2",
        "colab_type": "code",
        "outputId": "74a117cd-9b76-4d8b-b722-27375e347759",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 80
        }
      },
      "source": [
        "d = 1.5\n",
        "fd = fracdiff.frac_diff_ffd(fracdiff.frac_diff_ffd(rawclose.to_frame(), d), -d).dropna()\n",
        "fd"
      ],
      "execution_count": 51,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>close</th>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>date_time</th>\n",
              "      <th></th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "Empty DataFrame\n",
              "Columns: [close]\n",
              "Index: []"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 51
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "iqZd1vT1Rh2K",
        "colab_type": "code",
        "outputId": "d7d66f3e-5aff-4286-9214-fbd5558c915c",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 80
        }
      },
      "source": [
        "d = 0.5\n",
        "fd = fracdiff.frac_diff_ffd(fracdiff.frac_diff_ffd(rawclose.to_frame(), d), -d).dropna()\n",
        "fd"
      ],
      "execution_count": 52,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>close</th>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>date_time</th>\n",
              "      <th></th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "Empty DataFrame\n",
              "Columns: [close]\n",
              "Index: []"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 52
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "x8Q4HFOVRO_Z",
        "colab_type": "text"
      },
      "source": [
        "The result is that the series fd is all NaNs. The reason is when d is negative it takes an almost infinite number of observations for the weights to be lower than the threshold. That in turn leads to all the elements of the \"seriesF\" in frac_diff_ffd to have a value of NaNs.\n",
        "\n",
        "참고: https://github.com/jo-cho/research/blob/master/Chapter5/Chapter5_Exercises.ipynb"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "AElQET0IRno3",
        "colab_type": "text"
      },
      "source": [
        "## 5."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "t2yXWNlZRtd_",
        "colab_type": "text"
      },
      "source": [
        "### (a) Form a new series as a cumulative sum of log-prices."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "UTLJUNcSpFNy",
        "colab_type": "code",
        "outputId": "8587f8aa-0a53-46a4-e283-2b3c6b90029e",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "source": [
        "len(rawclose)"
      ],
      "execution_count": 112,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "58607"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 112
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "AxdbYV3mpIOc",
        "colab_type": "code",
        "outputId": "4a4931f2-1871-4bd0-d006-c17c08a2db97",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "source": [
        "close = rawclose[-5000:]\n",
        "len(close)"
      ],
      "execution_count": 113,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "5000"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 113
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "OGcugJ0GRw3j",
        "colab_type": "code",
        "outputId": "1492332e-f0fd-4386-e5ce-144d6e948e4f",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 136
        }
      },
      "source": [
        "cusumlog = np.cumsum(np.log(close))\n",
        "cusumlog.head()"
      ],
      "execution_count": 114,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "date_time\n",
              "2018-12-21 11:51:47     4.604270\n",
              "2018-12-21 11:54:29     9.209361\n",
              "2018-12-21 11:56:57    13.813229\n",
              "2018-12-21 11:58:14    18.415808\n",
              "2018-12-21 12:01:03    23.017975\n",
              "Name: close, dtype: float64"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 114
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "FgJBCdE0SXfq",
        "colab_type": "code",
        "outputId": "4877ace4-2496-4cff-deff-877c2ccb4ac9",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 302
        }
      },
      "source": [
        "cusumlog.plot()"
      ],
      "execution_count": 115,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.axes._subplots.AxesSubplot at 0x7f42ed047d68>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 115
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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6hfu7eywhhOgTdL8lUdfgID46kD/cm+LuUYQQos/R/ZZEnc2Bv5zNJIQQnaLL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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "FDaAu_86STkB",
        "colab_type": "text"
      },
      "source": [
        "### (b) Apply FFD, with 𝜏 = 1E − 5. Determine for what minimum d ∈ [0, 2] the new series is stationary."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "M7ZXuXavXCBN",
        "colab_type": "code",
        "outputId": "e8415992-1620-462a-e9fe-aab98656da86",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "source": [
        "for d in np.arange(0, 2.5, 0.05):\n",
        "    s = fracdiff.frac_diff_ffd(cusumlog.to_frame(),np.round(d,2)).dropna()\n",
        "    if len(s['close']) >= 2 :\n",
        "      p = adf(s['close'])[1]\n",
        "      if p<0.05:\n",
        "        print(\"minimum d is\", np.round(d,4), 'with p-value',p)\n",
        "        break"
      ],
      "execution_count": 116,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "minimum d is 2.0 with p-value 0.0\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "l5bLnqo1Z2_E",
        "colab_type": "text"
      },
      "source": [
        "### (c) Compute the correlation of the fracdiff series to the original (untransformed) series."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "iD6yngh3lkNe",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "fd = fracdiff.frac_diff_ffd(cusumlog.to_frame(), 2).dropna()"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "v7uixf5419gS",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "fdseries = fd.close"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "jI5xzdgRaLum",
        "colab_type": "code",
        "outputId": "14c8ea69-a7a8-4fbe-897d-53c75501f713",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 450
        }
      },
      "source": [
        "dffd = pd.concat({'original':close,'cusum':cusumlog,'fracdiff':fdseries},axis=1)\n",
        "dffd.dropna()"
      ],
      "execution_count": 122,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>original</th>\n",
              "      <th>cusum</th>\n",
              "      <th>fracdiff</th>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>date_time</th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>2018-12-21 11:56:57</th>\n",
              "      <td>99.8699</td>\n",
              "      <td>13.813229</td>\n",
              "      <td>-0.001223</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2018-12-21 11:58:14</th>\n",
              "      <td>99.7412</td>\n",
              "      <td>18.415808</td>\n",
              "      <td>-0.001290</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2018-12-21 12:01:03</th>\n",
              "      <td>99.7001</td>\n",
              "      <td>23.017975</td>\n",
              "      <td>-0.000412</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2018-12-21 12:02:10</th>\n",
              "      <td>99.8000</td>\n",
              "      <td>27.621143</td>\n",
              "      <td>0.001002</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2018-12-21 12:02:18</th>\n",
              "      <td>99.7900</td>\n",
              "      <td>32.224211</td>\n",
              "      <td>-0.000100</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>...</th>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2019-06-28 15:58:59</th>\n",
              "      <td>116.5600</td>\n",
              "      <td>23369.493569</td>\n",
              "      <td>-0.000858</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2019-06-28 15:59:02</th>\n",
              "      <td>116.5700</td>\n",
              "      <td>23374.252061</td>\n",
              "      <td>0.000086</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2019-06-28 15:59:45</th>\n",
              "      <td>116.5600</td>\n",
              "      <td>23379.010467</td>\n",
              "      <td>-0.000086</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2019-06-28 16:00:00</th>\n",
              "      <td>116.5700</td>\n",
              "      <td>23383.768959</td>\n",
              "      <td>0.000086</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2019-06-28 17:29:22</th>\n",
              "      <td>116.5700</td>\n",
              "      <td>23388.527451</td>\n",
              "      <td>0.000000</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "<p>4998 rows × 3 columns</p>\n",
              "</div>"
            ],
            "text/plain": [
              "                     original         cusum  fracdiff\n",
              "date_time                                            \n",
              "2018-12-21 11:56:57   99.8699     13.813229 -0.001223\n",
              "2018-12-21 11:58:14   99.7412     18.415808 -0.001290\n",
              "2018-12-21 12:01:03   99.7001     23.017975 -0.000412\n",
              "2018-12-21 12:02:10   99.8000     27.621143  0.001002\n",
              "2018-12-21 12:02:18   99.7900     32.224211 -0.000100\n",
              "...                       ...           ...       ...\n",
              "2019-06-28 15:58:59  116.5600  23369.493569 -0.000858\n",
              "2019-06-28 15:59:02  116.5700  23374.252061  0.000086\n",
              "2019-06-28 15:59:45  116.5600  23379.010467 -0.000086\n",
              "2019-06-28 16:00:00  116.5700  23383.768959  0.000086\n",
              "2019-06-28 17:29:22  116.5700  23388.527451  0.000000\n",
              "\n",
              "[4998 rows x 3 columns]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 122
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "wHFpmvWBbQPo",
        "colab_type": "code",
        "outputId": "6b305743-d0a2-4ee5-974e-a8a83bf7f024",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 142
        }
      },
      "source": [
        "dffd.dropna(inplace=True)\n",
        "dffd.corr()"
      ],
      "execution_count": 123,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
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              "\n",
              "    .dataframe tbody tr th {\n",
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              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>original</th>\n",
              "      <th>cusum</th>\n",
              "      <th>fracdiff</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>original</th>\n",
              "      <td>1.000000</td>\n",
              "      <td>0.933522</td>\n",
              "      <td>0.013149</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>cusum</th>\n",
              "      <td>0.933522</td>\n",
              "      <td>1.000000</td>\n",
              "      <td>0.001864</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>fracdiff</th>\n",
              "      <td>0.013149</td>\n",
              "      <td>0.001864</td>\n",
              "      <td>1.000000</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "          original     cusum  fracdiff\n",
              "original  1.000000  0.933522  0.013149\n",
              "cusum     0.933522  1.000000  0.001864\n",
              "fracdiff  0.013149  0.001864  1.000000"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 123
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "PVU-wswWbTBM",
        "colab_type": "text"
      },
      "source": [
        "### (d) Apply an Engel-Granger cointegration test on the original and fracdiff series. Are they cointegrated? Why?"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "5jc00LYUcz4U",
        "colab_type": "code",
        "outputId": "508b1906-b2bc-4a97-917f-cc5ce28ba098",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 68
        }
      },
      "source": [
        "from statsmodels.tsa.stattools import coint\n",
        "\n",
        "coint = coint(dffd['original'], dffd['fracdiff'], autolag='AIC')\n",
        "coint"
      ],
      "execution_count": 124,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(-0.7550145444612716,\n",
              " 0.9403643885314109,\n",
              " array([-3.89863304, -3.33735303, -3.04529886]))"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 124
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "0gt80JzHdWvh",
        "colab_type": "code",
        "outputId": "f777114a-77c5-4ac6-993b-b57d435555bf",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 51
        }
      },
      "source": [
        "print('p-value: {}'.format(coint[1]),'\\n','they are not cointegrated')"
      ],
      "execution_count": 125,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "p-value: 0.9403643885314109 \n",
            " they are not cointegrated\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "LBUs73L6d1qJ",
        "colab_type": "text"
      },
      "source": [
        "why??"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "jlsadgn_d3I6",
        "colab_type": "text"
      },
      "source": [
        "### (e) Apply a Jarque-Bera normality test on the fracdiff series"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "4LszSk4geTqb",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "from scipy.stats import jarque_bera"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "aD-YDtE8doPN",
        "colab_type": "code",
        "outputId": "046e5519-4f56-46a2-e826-ecfdb7f424ee",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "source": [
        "jb_test = jarque_bera(fdseries)\n",
        "print('P-value: {}'.format(jb_test[1]))"
      ],
      "execution_count": 127,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "P-value: 0.0\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "SnCV8LZPeS2U",
        "colab_type": "text"
      },
      "source": [
        "## 6. "
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "6I7YKdnFe2r_",
        "colab_type": "text"
      },
      "source": [
        "### (a) Apply a CUSUM filter (Chapter 2), where h is twice the standard deviation of the series."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "QSm8JR4Zp9P1",
        "colab_type": "code",
        "outputId": "9dde2548-c64e-42c0-c756-4f4a6327e29d",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 303
        }
      },
      "source": [
        "fdseries.plot()"
      ],
      "execution_count": 128,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.axes._subplots.AxesSubplot at 0x7f42ecfc3f60>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 128
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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w37DjmwBfUlObA26a9iUIInAQeM+rRVtjTUhJMPuZibi4aRo/f2k/ACBDJHO+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\nt3HzYIwx5rb/AGwUUmWvc3diAAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "GzGGNvYjq5cK",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "fdseries2 = fdseries.copy()"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "c0Fr8_YqCoVg",
        "colab_type": "code",
        "outputId": "f58c226b-19d7-4fb8-8555-babd06d7950c",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "source": [
        "fdseries2.std()"
      ],
      "execution_count": 130,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.001421347900053483"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 130
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "GD8h3E4me8OK",
        "colab_type": "code",
        "outputId": "a12bac8a-fc44-41db-e178-336f3ef99735",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 275
        }
      },
      "source": [
        "h = 2*fdseries2.std()\n",
        "t_events = filters.cusum_filter(fdseries2,h)\n",
        "t_events"
      ],
      "execution_count": 131,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "/usr/local/lib/python3.6/dist-packages/pandas/core/algorithms.py:1977: RuntimeWarning: invalid value encountered in subtract\n",
            "  out_arr[res_indexer] = arr[res_indexer] - arr[lag_indexer]\n"
          ],
          "name": "stderr"
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "DatetimeIndex(['2018-12-21 12:23:55', '2018-12-21 12:33:31',\n",
              "               '2018-12-21 12:35:19', '2018-12-21 12:39:29',\n",
              "               '2018-12-21 12:46:14', '2018-12-21 12:46:56',\n",
              "               '2018-12-21 12:48:32', '2018-12-21 13:00:50',\n",
              "               '2018-12-21 13:26:52', '2018-12-21 13:41:55',\n",
              "               ...\n",
              "               '2019-06-27 10:09:28', '2019-06-27 10:51:55',\n",
              "               '2019-06-27 12:35:23', '2019-06-27 13:07:45',\n",
              "               '2019-06-27 14:08:04', '2019-06-28 12:20:41',\n",
              "               '2019-06-28 12:39:45', '2019-06-28 15:53:24',\n",
              "               '2019-06-28 15:58:18', '2019-06-28 17:29:22'],\n",
              "              dtype='datetime64[ns]', length=1382, freq=None)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 131
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "p6w9OmjEes6s",
        "colab_type": "text"
      },
      "source": [
        "\n",
        "### (b) Use the filtered timestamps to sample a features’ matrix. Use as one of the features the fracdiff value.\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "GJXSUy0DkCaE",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 255
        },
        "outputId": "687abea4-8a1a-469e-990c-29987ae3c9e0"
      },
      "source": [
        "close_feat = close.loc[t_events]\n",
        "fd_feat = fdseries.loc[t_events]\n",
        "ft = (pd.DataFrame().assign(d_feat=close_feat, fd_feat=fd_feat).drop_duplicates().dropna())\n",
        "print(ft)"
      ],
      "execution_count": 132,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "                       d_feat   fd_feat\n",
            "2018-12-21 12:23:55   99.4000  0.000241\n",
            "2018-12-21 12:33:31   99.2550  0.000958\n",
            "2018-12-21 12:35:19   99.2902  0.000355\n",
            "2018-12-21 12:39:29   99.4200  0.001292\n",
            "2018-12-21 12:46:14   99.4210  0.000402\n",
            "...                       ...       ...\n",
            "2019-06-28 12:20:41  116.4800  0.000772\n",
            "2019-06-28 12:39:45  116.5567  0.000658\n",
            "2019-06-28 15:53:24  116.4400  0.000601\n",
            "2019-06-28 15:58:18  116.6600  0.001888\n",
            "2019-06-28 17:29:22  116.5700  0.000000\n",
            "\n",
            "[1381 rows x 2 columns]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "qH2qgArq_ubL",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 238
        },
        "outputId": "0aa89d2e-e043-4ce4-c9c8-f4756116d891"
      },
      "source": [
        "mlfinlab.sampling.concurrent.num_concurrent_events(fdseries.index, events.t1, molecule=events.index )"
      ],
      "execution_count": 133,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "date_time\n",
              "2019-02-27 14:45:01     1\n",
              "2019-02-27 14:54:53     1\n",
              "2019-02-27 15:10:13     0\n",
              "2019-02-27 15:13:14     1\n",
              "2019-02-27 15:26:57     1\n",
              "                       ..\n",
              "2019-06-28 15:58:59    14\n",
              "2019-06-28 15:59:02    14\n",
              "2019-06-28 15:59:45    14\n",
              "2019-06-28 16:00:00    14\n",
              "2019-06-28 17:29:22    15\n",
              "Length: 1966, dtype: int64"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 133
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "fVHHuCABpn6M",
        "colab_type": "text"
      },
      "source": [
        "### (c) Form labels using the triple-barrier method, with symmetric horizontal barriers of twice the daily standard deviation, and a vertical barrier of 5 days."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "T_uSGGKrt07N",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "from mlfinlab import util"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "NCNPVrDPuhRn",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "target = util.get_daily_vol(fdseries)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "RcbdTH3Grw9A",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "vertical_barrier_times = labeling.add_vertical_barrier(t_events, fdseries, num_days=5)\n",
        "pt_sl = [2,2]"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "AZbJKA1NzPFm",
        "colab_type": "code",
        "outputId": "9e1f9ac0-06a8-4987-ab26-ea30a347fb95",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 136
        }
      },
      "source": [
        "# Get Events\n",
        "events = labeling.get_events(fdseries, t_events, pt_sl, target, min_ret=0.001, num_threads=1, vertical_barrier_times=vertical_barrier_times )"
      ],
      "execution_count": 137,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "/usr/local/lib/python3.6/dist-packages/mlfinlab/labeling/labeling.py:124: FutureWarning: \n",
            "Passing list-likes to .loc or [] with any missing label will raise\n",
            "KeyError in the future, you can use .reindex() as an alternative.\n",
            "\n",
            "See the documentation here:\n",
            "https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#deprecate-loc-reindex-listlike\n",
            "  target = target.loc[t_events]\n"
          ],
          "name": "stderr"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "wKkKVdrc2vIi",
        "colab_type": "code",
        "outputId": "8cf765d7-b0ba-4b79-aa51-fe8afe40e520",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 204
        }
      },
      "source": [
        "events.head()"
      ],
      "execution_count": 138,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<div>\n",
              "<style scoped>\n",
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              "\n",
              "    .dataframe thead th {\n",
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              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>t1</th>\n",
              "      <th>trgt</th>\n",
              "      <th>pt</th>\n",
              "      <th>sl</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>2018-12-24 09:41:26</th>\n",
              "      <td>2018-12-31 09:30:00</td>\n",
              "      <td>174.920163</td>\n",
              "      <td>2</td>\n",
              "      <td>2</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2018-12-24 09:59:28</th>\n",
              "      <td>2018-12-31 09:30:00</td>\n",
              "      <td>106.421025</td>\n",
              "      <td>2</td>\n",
              "      <td>2</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2018-12-24 10:00:13</th>\n",
              "      <td>2018-12-31 09:30:00</td>\n",
              "      <td>104.302552</td>\n",
              "      <td>2</td>\n",
              "      <td>2</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2018-12-24 10:01:39</th>\n",
              "      <td>2018-12-31 09:30:00</td>\n",
              "      <td>101.489368</td>\n",
              "      <td>2</td>\n",
              "      <td>2</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2018-12-24 10:11:27</th>\n",
              "      <td>2018-12-31 09:30:00</td>\n",
              "      <td>93.148346</td>\n",
              "      <td>2</td>\n",
              "      <td>2</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "                                     t1        trgt  pt  sl\n",
              "2018-12-24 09:41:26 2018-12-31 09:30:00  174.920163   2   2\n",
              "2018-12-24 09:59:28 2018-12-31 09:30:00  106.421025   2   2\n",
              "2018-12-24 10:00:13 2018-12-31 09:30:00  104.302552   2   2\n",
              "2018-12-24 10:01:39 2018-12-31 09:30:00  101.489368   2   2\n",
              "2018-12-24 10:11:27 2018-12-31 09:30:00   93.148346   2   2"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 138
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "QGbPa_rSB-v1",
        "colab_type": "code",
        "outputId": "9ef4c7c9-484d-4e4a-e0c8-71be5abdcb9a",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 207
        }
      },
      "source": [
        "bins = labeling.get_bins(events, fdseries)\n",
        "bins['bin'].value_counts()"
      ],
      "execution_count": 139,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "/usr/local/lib/python3.6/dist-packages/mlfinlab/labeling/labeling.py:232: RuntimeWarning: divide by zero encountered in log\n",
            "  out_df['ret'] = np.log(prices.loc[events_['t1'].values].values) - np.log(prices.loc[events_.index])\n",
            "/usr/local/lib/python3.6/dist-packages/mlfinlab/labeling/labeling.py:232: RuntimeWarning: invalid value encountered in log\n",
            "  out_df['ret'] = np.log(prices.loc[events_['t1'].values].values) - np.log(prices.loc[events_.index])\n",
            "/usr/local/lib/python3.6/dist-packages/pandas/core/series.py:856: RuntimeWarning: divide by zero encountered in log\n",
            "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
          ],
          "name": "stderr"
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              " 0    1307\n",
              " 1      30\n",
              "-1      11\n",
              "Name: bin, dtype: int64"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 139
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "CPU9kEhKpqQ8",
        "colab_type": "text"
      },
      "source": [
        "### (d) Fit a bagging classifier of decision trees where:\n",
        "\n",
        "(i) The observed features are bootstrapped using the sequential method from Chapter 4. \n",
        "\n",
        "(ii) On each bootstrapped sample, sample weights are determined using the techniques from Chapter 4."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "r1sVV5T-8V4K",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "from mlfinlab.sampling.bootstrapping import get_ind_mat_average_uniqueness, get_ind_matrix, seq_bootstrap\n",
        "from mlfinlab.sampling.concurrent import get_av_uniqueness_from_triple_barrier"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "FyB1IpfY8ljU",
        "colab_type": "code",
        "outputId": "da5eb3d5-f62d-44df-d93f-fdc760b59635",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 453
        }
      },
      "source": [
        "av_uniq = get_av_uniqueness_from_triple_barrier(events, fdseries, 3)\n",
        "av_uniq"
      ],
      "execution_count": 141,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "2019-12-16 09:47:08.805292 100.0% num_concurrent_events done after 0.02 minutes. Remaining 0.0 minutes.\n",
            "2019-12-16 09:47:09.745162 100.0% _get_average_uniqueness done after 0.01 minutes. Remaining 0.0 minutes.\n"
          ],
          "name": "stderr"
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
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              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
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              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>tW</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>2018-12-24 09:41:26</th>\n",
              "      <td>0.035665</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2018-12-24 09:59:28</th>\n",
              "      <td>0.022339</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2018-12-24 10:00:13</th>\n",
              "      <td>0.021738</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2018-12-24 10:01:39</th>\n",
              "      <td>0.021346</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2018-12-24 10:11:27</th>\n",
              "      <td>0.019019</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>...</th>\n",
              "      <td>...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2019-06-28 12:20:41</th>\n",
              "      <td>NaN</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2019-06-28 12:39:45</th>\n",
              "      <td>NaN</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2019-06-28 15:53:24</th>\n",
              "      <td>NaN</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2019-06-28 15:58:18</th>\n",
              "      <td>NaN</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2019-06-28 17:29:22</th>\n",
              "      <td>NaN</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "<p>1363 rows × 1 columns</p>\n",
              "</div>"
            ],
            "text/plain": [
              "                           tW\n",
              "2018-12-24 09:41:26  0.035665\n",
              "2018-12-24 09:59:28  0.022339\n",
              "2018-12-24 10:00:13  0.021738\n",
              "2018-12-24 10:01:39  0.021346\n",
              "2018-12-24 10:11:27  0.019019\n",
              "...                       ...\n",
              "2019-06-28 12:20:41       NaN\n",
              "2019-06-28 12:39:45       NaN\n",
              "2019-06-28 15:53:24       NaN\n",
              "2019-06-28 15:58:18       NaN\n",
              "2019-06-28 17:29:22       NaN\n",
              "\n",
              "[1363 rows x 1 columns]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 141
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "qXvf7qx8-FUd",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "18f955c0-0d66-427e-b7af-e744ea253dbb"
      },
      "source": [
        "# get avg uniqueness for bootstrapping\n",
        "max_samples = av_uniq.mean()[0]\n",
        "max_samples"
      ],
      "execution_count": 142,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.036501273474702944"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 142
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "CzC1_z94-btk",
        "colab_type": "text"
      },
      "source": [
        "let's fit"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "kONqVVlv9eWm",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "from sklearn.preprocessing import label_binarize\n",
        "from sklearn.multiclass import OneVsRestClassifier\n",
        "from scipy import interp\n",
        "\n",
        "from sklearn import datasets\n",
        "from sklearn import metrics\n",
        "from sklearn.metrics import roc_curve, auc\n",
        "from sklearn.model_selection import train_test_split\n",
        "from sklearn.tree import DecisionTreeClassifier\n",
        "from sklearn.ensemble import RandomForestClassifier, ExtraTreesClassifier, BaggingClassifier\n",
        "from itertools import cycle"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "umQMe1Gk-60t",
        "colab_type": "text"
      },
      "source": [
        " model data"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "DeHCXsNk-eVe",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 419
        },
        "outputId": "a4324e50-5d3b-4cb0-ee95-dc32e16d72bf"
      },
      "source": [
        "data = ft.join(av_uniq,how='left').join(bins.bin,how='left').dropna()\n",
        "data"
      ],
      "execution_count": 144,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
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              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>d_feat</th>\n",
              "      <th>fd_feat</th>\n",
              "      <th>tW</th>\n",
              "      <th>bin</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>2018-12-24 09:41:26</th>\n",
              "      <td>97.1233</td>\n",
              "      <td>0.000137</td>\n",
              "      <td>0.035665</td>\n",
              "      <td>0.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2018-12-24 09:59:28</th>\n",
              "      <td>96.4218</td>\n",
              "      <td>0.001264</td>\n",
              "      <td>0.022339</td>\n",
              "      <td>0.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2018-12-24 10:00:13</th>\n",
              "      <td>96.4800</td>\n",
              "      <td>0.000603</td>\n",
              "      <td>0.021738</td>\n",
              "      <td>0.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2018-12-24 10:01:39</th>\n",
              "      <td>96.4980</td>\n",
              "      <td>0.000187</td>\n",
              "      <td>0.021346</td>\n",
              "      <td>0.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2018-12-24 10:11:27</th>\n",
              "      <td>96.2700</td>\n",
              "      <td>0.002392</td>\n",
              "      <td>0.019019</td>\n",
              "      <td>0.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>...</th>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2019-06-21 15:23:05</th>\n",
              "      <td>116.5000</td>\n",
              "      <td>0.000429</td>\n",
              "      <td>0.070297</td>\n",
              "      <td>0.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2019-06-21 15:41:24</th>\n",
              "      <td>116.5067</td>\n",
              "      <td>0.000058</td>\n",
              "      <td>0.038846</td>\n",
              "      <td>0.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2019-06-21 15:44:05</th>\n",
              "      <td>116.5200</td>\n",
              "      <td>0.000114</td>\n",
              "      <td>0.073228</td>\n",
              "      <td>0.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2019-06-27 10:51:55</th>\n",
              "      <td>115.7098</td>\n",
              "      <td>0.000018</td>\n",
              "      <td>0.111111</td>\n",
              "      <td>0.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2019-06-27 13:07:45</th>\n",
              "      <td>115.8300</td>\n",
              "      <td>0.000086</td>\n",
              "      <td>0.092208</td>\n",
              "      <td>0.0</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "<p>1347 rows × 4 columns</p>\n",
              "</div>"
            ],
            "text/plain": [
              "                       d_feat   fd_feat        tW  bin\n",
              "2018-12-24 09:41:26   97.1233  0.000137  0.035665  0.0\n",
              "2018-12-24 09:59:28   96.4218  0.001264  0.022339  0.0\n",
              "2018-12-24 10:00:13   96.4800  0.000603  0.021738  0.0\n",
              "2018-12-24 10:01:39   96.4980  0.000187  0.021346  0.0\n",
              "2018-12-24 10:11:27   96.2700  0.002392  0.019019  0.0\n",
              "...                       ...       ...       ...  ...\n",
              "2019-06-21 15:23:05  116.5000  0.000429  0.070297  0.0\n",
              "2019-06-21 15:41:24  116.5067  0.000058  0.038846  0.0\n",
              "2019-06-21 15:44:05  116.5200  0.000114  0.073228  0.0\n",
              "2019-06-27 10:51:55  115.7098  0.000018  0.111111  0.0\n",
              "2019-06-27 13:07:45  115.8300  0.000086  0.092208  0.0\n",
              "\n",
              "[1347 rows x 4 columns]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 144
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "jw7fNfdg_Lo2",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "X = data.iloc[:,:-1].values # features\n",
        "y = data.iloc[:,-1].values.reshape(-1,1) # bin"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "S0yD9k46psj5",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.3,\n",
        "                                                    shuffle=False)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "nhatzLio_pXu",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "dtclf = DecisionTreeClassifier(criterion='entropy',max_features='auto',\n",
        "                                  class_weight='balanced')\n",
        "\n",
        "bclf = BaggingClassifier(base_estimator=dtclf, n_estimators=1000,\n",
        "                       max_samples= max_samples, max_features=1.)\n",
        "\n",
        "clf = OneVsRestClassifier(bclf)\n",
        "\n",
        "fit = clf.fit(X_train,y_train)\n",
        "\n",
        "#train"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "12TgggjrDJ7E",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 241
        },
        "outputId": "5ca9cc39-8fbe-43b0-8c7b-e1000cf6d80f"
      },
      "source": [
        "y_pred = fit.predict(X)\n",
        "print(metrics.classification_report(y, y_pred))"
      ],
      "execution_count": 148,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "              precision    recall  f1-score   support\n",
            "\n",
            "        -1.0       0.00      0.00      0.00        11\n",
            "         0.0       0.97      1.00      0.98      1306\n",
            "         1.0       0.00      0.00      0.00        30\n",
            "\n",
            "    accuracy                           0.97      1347\n",
            "   macro avg       0.32      0.33      0.33      1347\n",
            "weighted avg       0.94      0.97      0.95      1347\n",
            "\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "stream",
          "text": [
            "/usr/local/lib/python3.6/dist-packages/sklearn/metrics/classification.py:1437: UndefinedMetricWarning: Precision and F-score are ill-defined and being set to 0.0 in labels with no predicted samples.\n",
            "  'precision', 'predicted', average, warn_for)\n"
          ],
          "name": "stderr"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Xyfwl0aYGxJy",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        ""
      ],
      "execution_count": 0,
      "outputs": []
    }
  ]
}